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REVIEW 4 major objections 4 minor 27 references

On rationality of certain Eisenstein cohomology

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read For balanced degenerate principal series, the Eisenstein map to sheaf cohomology is equivariant under every automorphism of C.

desk verdict New and useful rationality theorem for degenerate principal series, with an explicit computational core and one load-bearing vanishing assertion that needs a real proof. read the letter →

arxiv 2506.06738 v2 pith:TF3HB4D3 submitted 2025-06-07 math.NT math.RT

Yubo Jin , Dongwen Liu , Binyong Sun This is my paper
classification math.NTmath.RT MSC 11F75
keywords EisensteincohomologydegenerateprincipalseriesrationalityautomorphicformsGaloisactionrelativeLiealgebraHeckecharacterGL_n
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to prove that the Eisenstein map attached to degenerate principal series representations of $\mathrm{GL}_n$ over a totally imaginary number field containing a CM subfield is equivariant under the action of every automorphism of $\mathbb{C}$, at the bottom degree of cohomology. If the theorem is right, the bottom-degree Eisenstein cohomology acquires a rational structure over the field generated by the values of the defining Hecke character, the same kind of arithmetic information that the principal-series case already provided. The authors state that this will be used in forthcoming work to study rationality of special values of $L$-functions. The result covers the balanced range of infinity types and treats the degenerate principal series, where the local representations remain irreducible under the balanced assumption.

What carries the argument

The object that carries the argument is the degenerate principal series representation $I_\eta = \mathrm{uInd}_{P_n(\mathbb{A})}^{\mathrm{GL}_n(\mathbb{A})}(1 \otimes \eta^{-1})$ together with the associated Eisenstein map $\mathrm{Eis}_\eta$ induced by the holomorphic Eisenstein series. At the bottom degree $c_n = ([k:\mathbb{Q}]/2)(n-1)$, the source cohomology space is one-dimensional, so the proof can follow an explicit generator; the $\mathrm{Aut}(\mathbb{C})$-action on that line is controlled by the normalized intertwining operators and by the scalars $\nabla_k^{k-n}$, which are made Galois-compatible through the rationality of the critical values of $L(s,\eta)$ at $s=0,-1,\ldots,-n$. The final argument uses the boundary restriction to the Borel stratum and the vanishing of $\mathrm{Hom}_{\mathrm{GL}_n(\mathbb{A}_f)}(I_{\eta,f}, \ker(r_{B_n}))$ to force the difference of the two routes around the equivariance diagram to be zero.

What would settle it

A concrete way to test the claim: compute the Hom space $\mathrm{Hom}_{\mathrm{GL}_n(\mathbb{A}_f)}(I_{\eta,f}, \ker(r_{B_n}))$ for a small balanced example, say $n=2$ over an imaginary quadratic field with a chosen algebraic Hecke character $\eta$ satisfying the balanced condition, and try to exhibit a nonzero equivariant map. Alternatively, for any $\sigma \in \mathrm{Aut}(\mathbb{C})$, evaluate the difference map $\Delta_\sigma$ on the explicit generator constructed in Section 5.1 and check whether its Borel boundary restriction vanishes; a nonzero value would falsify the theorem, while a complete vanishing proof for this Hom space would supply the missing step.

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Extended reading notes

Core claim

The paper's central claim is Theorem 1.1: for an algebraic Hecke character $\eta$ satisfying the balanced condition $\min_\iota \eta_\iota \le 0$ and $\max_\iota \eta_\iota \ge n$ at every archimedean place, the Eisenstein map $\mathrm{Eis}_\eta$ from $H^{c_n}(\mathfrak{g}_{n,\infty}, \tilde K_{n,\infty}; I_\eta \otimes F_\eta^\vee)$ to $H^{c_n}(X_n, F_\eta^\vee)$ is $\mathrm{Aut}(\mathbb{C})$-equivariant. For each $\sigma \in \mathrm{Aut}(\mathbb{C})$, the $\sigma$-linear actions on both spaces are built from the twisted character $^\sigma\eta$ and fixed highest-weight identifications, and the theorem asserts that the diagram (1.8) commutes. The proof constructs an explicit generator of the one-dimensional source, computes its image through the constant-term formula as a sum of normalized intertwining operators, checks equivariance after multiplying by the discriminant factor $\nabla_k^{k-n}$, and then kills the remaining difference map by showing it must land in the kernel of the Borel boundary restriction. In consequence, the bottom-degree Eisenstein cohomology carries a $\mathbb{Q}(\eta)$-rational structure in this degenerate principal-series setting.

Load-bearing premise

The whole proof leans on the assertion, imported from the principal-series case without proof here, that there is no nonzero $\mathrm{GL}_n(\mathbb{A}_f)$-equivariant map from $I_{\eta,f}$ into the kernel of the Borel boundary restriction; if that vanishing fails for some balanced $\eta$, the $\mathrm{Aut}(\mathbb{C})$-equivariance of the Eisenstein map does not follow.

Editorial extensions

If this is right

  • The bottom-degree Eisenstein cohomology $H^{c_n}(X_n, F_\eta^\vee)$ carries a $\mathbb{Q}(\eta)$-rational structure, so Galois conjugates of Eisenstein classes remain Eisenstein.
  • The rational structure gives a well-defined notion of rational Eisenstein classes in this cohomology, the object needed for period comparisons and special-value formulas.
  • The $\mathrm{Aut}(\mathbb{C})$-equivariance of the cohomological intertwining operators, with the discriminant normalization, gives a Galois-compatible description of constant terms along the Borel stratum.
  • The authors state that the present theorem will be used in forthcoming work to prove rationality of special values of $L$-functions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The method suggests that the same $\mathrm{Aut}(\mathbb{C})$-equivariance should extend to higher-degree Eisenstein cohomology whenever the relevant cohomology spaces are small enough to track an explicit generator, not just the bottom degree.
  • The missing Hom-vanishing step could be supplied by a purely local argument: if $\ker(r_{B_n})$ admits a filtration whose graded pieces have no $I_{\eta,f}$-coinvariants, the theorem would become unconditional.
  • A testable numerical consequence: for $n=2$ over an imaginary quadratic field, the Galois conjugate of a balanced Eisenstein class should have periods differing from the original by the predicted discriminant-type factors, which could be checked in explicit boundary-cohomology computations.
  • If the balanced condition fails, local degenerate principal series may become reducible and the Eisenstein map may acquire poles at $s=0$; the rationality statement would then likely need to be replaced by one about residues or regularized values.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper studies Eisenstein cohomology for GL_n over a totally imaginary field k, in the bottom degree c_n, for degenerate principal series representations induced from the maximal parabolic P_n of type (n-1,1). Under a balanced condition (1.4) on an algebraic Hecke character η, it claims that the Eisenstein map Eis_η at s=0 is Aut(C)-equivariant (Theorem 1.1), thereby providing a Q(η)-rational structure on the image in the bottom-degree cohomology. The proof computes the constant term of the degenerate Eisenstein series, identifies the relevant relative Lie algebra cohomology with a one-dimensional space generated by an explicit vector, proves Aut(C)-equivariance of the normalized intertwining operators up to the scalar ∇_k^{k-n}, and then reduces the main theorem to a vanishing statement for Hom_{GL_n(A_f)}(I_{η,f}, ker r_{B_n}).

Significance. If completed, the result is significant: it extends Harder's rationality theorem [Har90] from principal series to the degenerate principal series in the balanced case, and the authors state that it will be used for rationality of special L-values. The paper's concrete strengths are the explicit constant-term formula (2.11), the explicit generator construction (5.2)-(5.3) with the local integral computation of Lemma 5.4, and the reduction of the archimedean equivariance to a finite intertwiner computation. The non-archimedean equivariance is imported from [HR20, Wal03], which is reasonable. However, the central theorem is not yet fully established because the final vanishing assertion is unproved, and a key local lemma (Lemma 5.2) is stated without proof.

major comments (4)
  1. [Section 5.3, final paragraph] The proof of Theorem 1.1 hinges on the assertion that Hom_{GL_n(A_f)}(I_{η,f}, ker(r_{B_n})) = {0}, stated as 'The proof in [Har90, Theorem II] shows'. This is not established in the manuscript. The representation I_{η,f} is induced from the maximal parabolic P_n of type (n-1,1), whereas [Har90, Theorem II] is formulated for principal series induced from the Borel. Since I_{η,f} embeds into the Borel induction I^{B,(n)}_{η,f}, the desired vanishing would indeed follow if Harder's argument proves the analogous vanishing for the full principal series, but the paper neither verifies that the cited argument yields this stronger statement nor supplies a proof for the degenerate parabolic case. Because Δ_σ is nonzero exactly when this Hom space is nonzero, this gap is load-bearing for the Aut(C)-equivariance claim. The authors should either prove the vanishing or give a precise reference with the exact statement covering their representation.
  2. [Section 5.1, Lemma 5.2] Lemma 5.2 is stated without proof. It asserts the existence and uniqueness of a lowest-weight vector of the form (5.2), and this vector is used to define the explicit generator κ_{η,v} in (5.3). The subsequent equivariance computation (Lemma 5.5 and Proposition 5.3) depends on the specific normalization in (5.2), so this omission is not merely cosmetic. The sentence 'We have the following lemma by the fact that τ_{η,v} is the Cartan component of τ_{n,v} ⊗ τ'^∨_{η,v}' is not a complete proof. Please provide the full argument or a precise citation.
  3. [Section 3.4, Lemma 3.1] The proof of Lemma 3.1 is too terse for a load-bearing identification. The argument reduces the isomorphism to the assertion that the inclusion 1 ↪ uInd^{GL_{n-1}(k_∞)}_{B_{n-1}(k_∞)} 1 induces an isomorphism on the one-dimensional H^0(m_{n,∞}; ...) spaces. This requires justification: the unnormalized induced module is not a direct sum, and the image of the inclusion could in principle vanish on the relevant invariant subspace. Please spell out the Frobenius reciprocity / dimension argument in detail, or give a reference that proves this precise statement.
  4. [Section 2, Proposition 2.1] In the proof of Proposition 2.1, the sentence 'It is easy to verify that the Hecke L-functions in (2.11) does not produce poles or zeros' is not adequate. At s=0 the constant-term formula involves the ratios L(k-n, η)/L(0, η) for k=1,...,n, and the proof of the holomorphy and nonvanishing of the Eisenstein map depends on these values being finite and on the ratios not making the leading term vanish. The authors should give the required argument for the L-values (for instance by citing the relevant critical-value theorem) rather than leaving it as an easy verification.
minor comments (4)
  1. [Section 3.3, after (3.10)] The phrase 'it is routine to check that the diagram ... commutes' after (3.10) would benefit from one explicit sentence describing how the normalization of (3.7) is respected by the σ-linear maps, since this is the point where the choice of the highest weight vector v_η matters.
  2. [Section 5.2, Lemma 5.5] The action of σ on the set W_{n,∞} and on the vectors w(n).v_η is used in diagram (5.12) but is not defined explicitly before Lemma 5.5. Please add a definition, e.g. via the action on the embeddings E_k and on the Weyl group componentwise.
  3. [Section 2.2, formula (2.10)] The notation in the definition of Λ^{(k)}_{η,s} uses '1' both for the trivial character and for the number one in exponents; this is a minor readability issue. Please distinguish the characters 1 and the integer 1, for instance by writing the trivial character as 𝟙.
  4. [Section 5.3, Proposition 5.6] The factor |δ_k|^{(n-k)/2} in the displayed formula for r'_{B_n}∘Eis'_η appears with a sign of the exponent opposite to that in (2.11); the consistency is probably correct because of the normalization of the intertwining operators, but a short comment would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is self-contained modulo standard external theorems; the unproved Harder vanishing assertion is a correctness gap, not a circular reduction.

full rationale

The main theorem (Theorem 1.1) asserts a commutativity property of the Eisenstein map with naturally defined Aut(C)-actions; neither the σ-actions nor the Eisenstein map are fitted to the cohomology being predicted. The constant-term computation in Section 2 is a direct Bruhat-unfolding calculation combined with Langlands' local intertwining formula (2.8)-(2.11), and the archimedean cohomology computations in Sections 3-4 use Delorme's lemma, Kostant's theorem, and external results of Harder/Raghuram/Waldspurger. The only same-author citation, [JLS24] in Lemma 5.1, supplies a translation functor for archimedean K-types; it is an independently posted/published result (arXiv:2412.18805, to appear in Adv. Math.) that does not contain the present theorem, so per the hard rules it is independent evidence and does not raise the circularity score. The genuine weak point is the final step of Section 5.3: 'The proof in [Har90, Theorem II] shows that Hom_{GL_n(A_f)}(I_{η,f}, ker(r_{B_n})) = {0}.' This asserts an unproved extension of Harder's principal-series vanishing to the degenerate principal-series representation I_{η,f}; if the extension fails, Theorem 1.1 does not follow. However, that is a correctness/verification gap in an external citation, not circularity: the vanishing is a separate premise, and the paper neither defines I_{η,f} in terms of the Eisenstein map's equivariance nor fits the claimed equivariance into the definition of the Hom space. No step in the proof has the form 'define X by Y and then predict Y from X,' and no fitted parameter is renamed as a prediction. Hence no significant circularity; score 0.

Assumptions & free parameters 0 free parameters · 10 assumptions · 0 invented entities

The central theorem rests on several substantial external results (Delorme, Kostant, van Est, Gourevitch, Hanzer-Muić, Harder, Waldspurger, Raghuram). No free parameters are fitted; the Hecke character eta is input data. The paper's own contribution is the explicit generator and intertwining computations, not new foundational objects.

assumptions (10)
  • standard math Delorme's lemma for relative Lie algebra cohomology of induced representations
    Used throughout Section 3 to compute H^q(g_{n,∞}, K̃_{n,∞}; I ⊗ F^∨) and to isolate the bottom-degree cohomology (e.g., after (1.5), (3.4), Lemma 3.1).
  • standard math Kostant's theorem on the cohomology of nilpotent Lie algebras
    Provides the decomposition (3.6) H^p(n_{n,∞},F_eta^∨) = ⊕_{l(w)=p} ∧^p n_w^* ⊗ C w.v_eta, used to compute the boundary cohomology (4.6) and to build the explicit generator in Section 5.
  • standard math van Est theorem identifying continuous cohomology of N(k)\N(A)/K_N with relative Lie algebra cohomology
    Used in Section 4.2 to rewrite sheaf cohomology of the Borel boundary stratum as unipotent cohomology, including the Galois-equivariance statement after (4.5).
  • domain assumption Gourevitch's irreducibility theorem for local degenerate principal series of GL(n)
    Invoked in Proposition 2.1 to conclude the degenerate principal series I_eta,v is irreducible under condition (1.4), helping rule out poles of the Eisenstein series at s=0.
  • domain assumption Holomorphy of normalized intertwining operators at s=0 (Hanzer-Muić, Lemma 6.13)
    Used in Proposition 2.1 to show the Eisenstein series E(g;phi_s,eta) is holomorphic at s=0 and that the Eisenstein map (2.12) is well defined.
  • domain assumption Harder's theorem on Galois equivariance of critical values of Hecke L-functions
    Used in Proposition 5.6 to show the scalar factor (i^{[k:Q]/2}Δ_k)^{(n-k)/2} L(k-n,eta)/L(0,eta) transforms correctly under sigma, a key step in the boundary map equivariance.
  • domain assumption Harder's vanishing theorem Hom_{GL_n(A_f)}(I_eta,f, ker r_{B_n}) = 0
    The final step of Theorem 1.1: the paper asserts the proof from [Har90, Theorem II] applies to degenerate principal series, but no proof is given.
  • domain assumption Waldspurger's rationality theorem for p-adic intertwining operators
    Used in Proposition 5.3 (after (5.8)) to establish Aut(C)-equivariance of the finite-part intertwining operator N_f(w_k).
  • domain assumption Raghuram's discriminant formula |δ_k|^{1/2} = c i^{[k:Q]/2} Δ_k ∇_k
    Used in (5.4) to separate the discriminant factor in the constant term formula, allowing the L-value equivariance theorem to be applied.
  • domain assumption Translation functor from the authors' previous paper [JLS24] for archimedean degenerate principal series
    Used in Lemma 5.1 to transfer the K-type computation for a special character eta_0 to a general eta; a self-cited external result.

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Pith. "Pith review of On rationality of certain Eisenstein cohomology." pith.science (2026). https://pith.science/paper/TF3HB4D3

@misc{pith2026250606738,
  author       = {Pith},
  title        = {Pith review of: On rationality of certain Eisenstein cohomology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TF3HB4D3}},
  note         = {Machine review of arXiv:2506.06738}
}
read the original abstract

In this paper, we study the Eisenstein cohomology coming from Eisenstein series associated to degenerate principal series representations and prove certain rationality result.

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Works this paper leans on

27 extracted references · 23 canonical work pages

  1. [1]

    Armand Borel and Nolan R. Wallach. Continuous cohomology, discrete subgroups, and representations of reductive groups , volume 67 of Mathematical Surveys and Monographs . American Mathematical Society, Providence, RI, second edition, 2000

    work page 2000

  2. [2]

    Algebraicity of ratios of R ankin- S elberg L -functions and applications to D eligne's conjecture, 2022

    Shih-Yu Chen. Algebraicity of ratios of R ankin- S elberg L -functions and applications to D eligne's conjecture, 2022. arXiv:2205.15382 https://arxiv.org/abs/2205.15382

    arXiv 2022

  3. [3]

    Clozel, Motifs et formes automorphes: applications du principe de fonctorialit\' e

    L. Clozel, Motifs et formes automorphes: applications du principe de fonctorialit\' e . (French) [Motives and automorphic forms: applications of the functoriality principle] Automorphic forms, Shimura varieties, and L-functions, Vol. I (Ann Arbor, MI, 1988), 77--159, Perspect. Math., 10, Academic Press, Boston, MA, 1990

    work page 1988

  4. [4]

    On the nonvanishing hypothesis for R ankin- S elberg convolutions for GL _n( C) GL _n( C)

    Chao-Ping Dong and Huajian Xue. On the nonvanishing hypothesis for R ankin- S elberg convolutions for GL _n( C) GL _n( C) . Represent. Theory , 21:151--171, 2017

    work page 2017

  5. [5]

    Composition series for degenerate principal series of GL (n)

    Dmitry Gourevitch. Composition series for degenerate principal series of GL (n) . C. R. Math. Acad. Sci. Soc. R. Can. , 39(1):1--12, 2017

    work page 2017

  6. [6]

    Eisenstein cohomology of arithmetic groups

    G\"unter Harder. Eisenstein cohomology of arithmetic groups. T he case GL _2 . Invent. Math. , 89(1):37--118, 1987

    work page 1987

  7. [7]

    Some results on the E isenstein cohomology of arithmetic subgroups of GL _n

    G\"unter Harder. Some results on the E isenstein cohomology of arithmetic subgroups of GL _n . In Cohomology of arithmetic groups and automorphic forms ( L uminy- M arseille, 1989) , volume 1447 of Lecture Notes in Math. , pages 85--153. Springer, Berlin, 1990

    work page 1989

  8. [8]

    Degenerate principal series representations of GL _n( ) and GL _n( )

    Roger Howe and Soo Teck Lee. Degenerate principal series representations of GL _n( ) and GL _n( ) . J. Funct. Anal. , 166(2):244--309, 1999

    work page 1999

Show all 27 references
  1. [9]

    On the images and poles of degenerate E isenstein series for GL (n, A_Q ) and GL (n, R)

    Marcela Hanzer and Goran Mui\'c. On the images and poles of degenerate E isenstein series for GL (n, A_Q ) and GL (n, R) . Amer. J. Math. , 137(4):907--951, 2015

    2015

  2. [10]

    Raghuram

    G\"unter Harder and A. Raghuram. Eisenstein cohomology for GL _N and the special values of R ankin- S elberg L -functions , volume 203 of Annals of Mathematics Studies . Princeton University Press, Princeton, NJ, 2020

    2020

  3. [11]

    Calculus of archimedean Rankin-Selberg integrals with recurrence relations

    Taku Ishii and Tadashi Miyazaki. Calculus of archimedean Rankin-Selberg integrals with recurrence relations. Represent. Theory 26 (2022), 714–763

    2022

  4. [12]

    Archimedean period relations for Rankin-Selberg convolutions, 2024

    Yubo Jin, Dongwen Liu, and Binyong Sun. Archimedean period relations for Rankin-Selberg convolutions, 2024. arXiv:2412.18805 https://arxiv.org/abs/2412.18805, to appear in Adv. Math

    2024 arXiv

  5. [13]

    Henry H. Kim. Automorphic L -functions. In Lectures on automorphic L -functions , volume 20 of Fields Inst. Monogr. , pages 97--201. Amer. Math. Soc., Providence, RI, 2004

    2004

  6. [14]

    Lie algebra cohomology and the generalized B orel- W eil theorem

    Bertram Kostant. Lie algebra cohomology and the generalized B orel- W eil theorem. Ann. of Math. (2) , 74:329--387, 1961

    1961

  7. [15]

    Langlands

    Robert P. Langlands. Euler products , volume 1 of Yale Mathematical Monographs . Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1967

    1971

  8. [16]

    Erez M. Lapid. A remark on E isenstein series. In Eisenstein series and applications , volume 258 of Progr. Math. , pages 239--249. Birkh\"auser Boston, Boston, MA, 2008

    2008

  9. [17]

    Low degree cohomologies of congruence groups

    Jian-Shu Li and Binyong Sun. Low degree cohomologies of congruence groups. Sci. China Math. 62 (2019), no. 11, 2287–2308

    2019

  10. [18]

    Correspondances de H owe sur un corps p -adique , volume 1291 of Lecture Notes in Mathematics

    Colette M glin, Marie-France Vign\' e ras, and Jean-Loup Waldspurger. Correspondances de H owe sur un corps p -adique , volume 1291 of Lecture Notes in Mathematics . Springer-Verlag, Berlin, 1987

    1987

  11. [19]

    On certain classes of unitary representations for split classical groups

    Goran Mui\'c. On certain classes of unitary representations for split classical groups. Canad. J. Math. , 59(1):148--185, 2007

    2007

  12. [20]

    K. R. Parthasarathy, R. Ranga Rao; V. S. Varadarajan. Representations of complex semi-simple Lie groups and Lie algebras. Ann. of Math. (2) 85 (1967), 383–429

    1967

  13. [21]

    Raghuram

    A. Raghuram. Eisenstein cohomology for (n) and the special values of Rankin-Selberg L-functions over a totally imaginary number field, 2022. arXiv:2207.03393 https://arxiv.org/abs/2207.03393

    2022 arXiv

  14. [22]

    Raghuram

    A. Raghuram. Notes on the arithmetic of H ecke L -functions. Proc. Indian Acad. Sci. Math. Sci. , 132(2):Paper No. 71, 37, 2022

    2022

  15. [23]

    Eisenstein series and automorphic L -functions , volume 58 of American Mathematical Society Colloquium Publications

    Freydoon Shahidi. Eisenstein series and automorphic L -functions , volume 58 of American Mathematical Society Colloquium Publications . American Mathematical Society, Providence, RI, 2010

    2010

  16. [24]

    Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen

    Joachim Schwermer. Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen. Lect. Notes in Maths. Vol. 988, Berlin–Heidelberg–New York 1983

    1983

  17. [25]

    A generalization of the Cartan-Leray spectral sequence II

    van Est. A generalization of the Cartan-Leray spectral sequence II. Indagationes Math. 20: (series A) 406-413 (1958)

    1958

  18. [26]

    Waldspurger

    J.-L. Waldspurger. La formule de P lancherel pour les groupes p -adiques (d'apr\`es H arish- C handra). J. Inst. Math. Jussieu , 2(2):235--333, 2003

    2003

  19. [27]

    A. V. Zelevinsky. Induced representations of reductive p -adic groups. II . O n irreducible representations of GL (n) . Ann. Sci. \'Ecole Norm. Sup. (4) , 13(2):165--210, 1980

    1980

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