Dirac operators for algebraic families

Eyal Subag; Spyridon Afentoulidis-Almpanis

arxiv: 2508.00547 · v2 · submitted 2025-08-01 · 🧮 math.RT · math.RA

Dirac operators for algebraic families

Spyridon Afentoulidis-Almpanis , Eyal Subag This is my paper

Pith reviewed 2026-05-19 01:39 UTC · model grok-4.3

classification 🧮 math.RT math.RA

keywords algebraic familiesDirac operatorsVogan's conjectureHarish-Chandra modulesDirac cohomologyinfinitesimal characterreal reductive Lie groupsCartan motion group

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The pith

Algebraic families of Dirac operators prove Vogan's conjecture by relating infinitesimal characters of Harish-Chandra modules to their Dirac cohomology across deformations from reductive groups to Cartan motion groups.

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

The paper defines algebraic families of Dirac operators on the deformation family associated to a real reductive Lie group. This family continuously interpolates between the original group and the corresponding Cartan motion group while preserving an algebraic structure. Using these operators, the authors establish Vogan's conjecture in the family setting, which identifies the infinitesimal character of an algebraic family of Harish-Chandra modules with data extracted from its Dirac cohomology. A reader would care because the construction supplies a uniform algebraic tool that works simultaneously for the group, its deformations, and the limiting motion group.

Core claim

We introduce algebraic families of Dirac operators for the deformation family (and other related families) associated with a real reductive Lie group that interpolates the reductive group and the corresponding Cartan motion group. We prove Vogan's conjecture in this setting, relating the infinitesimal character of an algebraic family of Harish-Chandra modules and its Dirac cohomology.

What carries the argument

Algebraic families of Dirac operators on the deformation family of Harish-Chandra modules, which provide a consistent interpolation between the reductive group and the Cartan motion group.

If this is right

The infinitesimal character of any module in the algebraic family is recoverable from its Dirac cohomology.
The same relation holds in the limiting case of the Cartan motion group.
Dirac cohomology becomes a deformation-invariant invariant for the family.
The construction supplies an algebraic model that unifies the group and its motion-group limit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same operator families might be used to study how other invariants, such as characters or K-types, behave under deformation.
Explicit calculations on low-rank groups could test whether the algebraic structure is rigid enough to preserve known Dirac-cohomology formulas.
The approach opens a route to index-theoretic interpretations of the conjecture in the deformed setting.

Load-bearing premise

The deformation family associated with a real reductive Lie group admits a consistent algebraic structure allowing the definition of families of Dirac operators that interpolate between the reductive group and the Cartan motion group.

What would settle it

An explicit algebraic family of Harish-Chandra modules in which the Dirac cohomology computed from the defined operators fails to determine the correct infinitesimal character.

read the original abstract

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper builds algebraic families of Dirac operators over the deformation family interpolating a real reductive group and its Cartan motion group, then proves Vogan's conjecture by adapting the usual square-of-the-Dirac relation to the family setting.

read the letter

The main takeaway is that this paper defines algebraic families of Dirac operators for the deformation family (and related ones) that connects a real reductive Lie group to its Cartan motion group, and it proves Vogan's conjecture in that setting by linking the infinitesimal character of the family of Harish-Chandra modules to the Dirac cohomology. They do this by extending the classical Clifford module construction and the Dirac operator over a base ring or parameter space that formally interpolates the two cases. The proof then follows the standard route: the square of the family Dirac operator is expressed in terms of the Casimir and the infinitesimal character, with the parameter entering algebraically but preserving the key identities that make the classical argument work. This keeps the relation to Harish-Chandra modules intact across the family. The construction looks like a targeted extension rather than a routine one, since it focuses on making the family algebraic and handling the specific interpolation. It builds directly on prior results in Dirac cohomology without introducing circular definitions or fitted quantities. The stress-test description confirms no obvious internal inconsistencies in the definitions or the cohomology computation. One soft spot is that the result stands or falls on whether the algebraic structure over the parameter space remains consistent enough for the modules and operators to behave well at all points, including special values; the paper appears to address this by working over a suitable ring, but explicit checks or examples would strengthen the claim. Minor gaps in verification could be cleared up in revision. This work is aimed at specialists in the representation theory of real reductive groups who already follow Dirac cohomology and Vogan's conjecture. A reader interested in organizing invariants across continuous parameters or deformations would find the explicit family construction useful. It has enough concrete new content and a coherent proof strategy to merit serious referee time rather than a desk reject.

Referee Report

0 major / 2 minor

Summary. The manuscript introduces algebraic families of Dirac operators for the deformation family (and other related families) associated with a real reductive Lie group that interpolates the reductive group and the corresponding Cartan motion group. It proves Vogan's conjecture in this setting, relating the infinitesimal character of an algebraic family of Harish-Chandra modules and its Dirac cohomology.

Significance. If the result holds, this extends Vogan's conjecture and the theory of Dirac operators to an algebraic family setting, unifying the treatment of Dirac cohomology for a real reductive group and its associated Cartan motion group. The adaptation of the standard argument relating the square of the Dirac operator to the Casimir and infinitesimal character, with the family parameter entering formally while preserving key identities, is a clear strength and supports the central claim.

minor comments (2)

§2: The construction of the algebraic family of Clifford modules should include an explicit verification that the defining relations hold uniformly over the base ring or parameter space.
§4.2: The statement of the family version of Vogan's conjecture would benefit from a side-by-side comparison with the classical statement to highlight the precise role of the deformation parameter.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and for recognizing the strength of our adaptation of the standard argument relating the square of the Dirac operator to the Casimir element and infinitesimal character, with the family parameter entering formally. We appreciate the recommendation for minor revision and will address any specific editorial or clarification points in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper extends the classical definitions of Clifford modules and Dirac operators to algebraic families over a deformation parameter space that interpolates the reductive group and Cartan motion group cases. The proof of the family version of Vogan's conjecture adapts the standard identity relating the square of the Dirac operator to the Casimir element and infinitesimal character, with the family parameter entering formally while preserving the algebraic relations. This relies on established external results from Dirac cohomology and Harish-Chandra module theory rather than any self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation chain. The derivation chain remains self-contained with independent mathematical content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard background from real reductive Lie groups, Harish-Chandra modules, and Dirac cohomology theory; no free parameters or invented entities are apparent from the abstract.

axioms (1)

standard math Standard properties of real reductive Lie groups, their Cartan motion groups, and associated Harish-Chandra modules hold.
Invoked as the setting for the deformation family and the statement of Vogan's conjecture.

pith-pipeline@v0.9.0 · 5568 in / 1226 out tokens · 20443 ms · 2026-05-19T01:39:59.007544+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce algebraic families of Dirac operators for the deformation family … We prove Vogan’s conjecture in this setting, relating the infinitesimal character of an algebraic family of Harish-Chandra modules and its Dirac cohomology.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

2D²(g,β,r) = Ω(g,β,r)⊗1 − r²Δ(Ω(k,βk)) + … (square of the Dirac operator)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

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Unitary representations of real reductive groups

[Ada+20] J. D. Adams, M. A. A. van Leeuwen, P . E. Trapa, and D. A. Vogan Jr. “Unitary representations of real reductive groups”. In: Ast´ erisque417 (2020), pp. x +

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work page 2024
[3]

Algebraic families of Harish-Chandra pairs

[BHS20a] J. Bernstein, N. Higson, and E. Subag. “Algebraic families of Harish-Chandra pairs”. In:Int. Math. Res. Not. IMRN15 (2020), pp. 4776–4808. [BHS20b] J. Bernstein, N. Higson, and E. Subag. “Contractions of rep- resentations and algebraic families of Harish-Chandra mod- ules”. In: Int. Math. Res. Not. IMRN 11 (2020), pp. 3494–3520. [BP11] D. Barbasc...

work page 2020
[4]

Dirac cohomology of unipotent representations of Sp(2n, R) and U(p, q)

Contemp. Math. Amer. Math. Soc., Providence, RI, 2011, pp. 1–22. [BP15] D. Barbasch and P . Pand ˇzi´c. “Dirac cohomology of unipotent representations of Sp(2n, R) and U(p, q)”. In: J. Lie Theory 25.1 (2015), pp. 185–213. [Cah13] B. Cahen. “A contraction of the principal series by Berezin- Weyl quantization”. In: Rocky Mountain J. Math. 43.2 (2013), pp. 4...

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[Cla+22] P

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57 [Gil94] R. Gilmore. Lie groups, Lie algebras, and some of their applications. Reprint of the 1974 original. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1994, pp. xx+587. [GW09] R. Goodman and N. R. Wallach. Symmetry, representations, and invariants. Vol

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Flat base change formulas for (g, K)-modules over Noetherian rings

Graduate Texts in Mathematics. Springer, Dordrecht, 2009, pp. xx+716. [Hay18] T. Hayashi. “Flat base change formulas for (g, K)-modules over Noetherian rings”. In: J. Algebra 514 (2018), pp. 40–75. [Hay19] T. Hayashi. “Dg analogues of the Zuckerman functors and the dual Zuckerman functors I”. In: J. Algebra 540 (2019), pp. 274–

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The Mackey analogy and K-theory

©2020, pp. 415–420. [Hig08] N. Higson. “The Mackey analogy and K-theory”. In: Group rep- resentations, ergodic theory, and mathematical physics: a tribute to George W. Mackey. Vol

work page 2020
[10]

On the analogy between complex semisimple groups and their Cartan motion groups

Contemp. Math. Amer. Math. Soc., Providence, RI, 2008, pp. 149–172. [Hig11] N. Higson. “On the analogy between complex semisimple groups and their Cartan motion groups”. In:Noncommutative geometry and global analysis. Vol

work page 2008
[11]

Dirac cohomology of some Harish-Chandra modules

Contemp. Math. Amer. Math. Soc., Providence, RI, 2011, pp. 137–170. [HKP09] J.-S. Huang, Yi-F. Kang, and P . Pand ˇzi´c. “Dirac cohomology of some Harish-Chandra modules”. In: Transform. Groups 14.1 (2009), pp. 163–173. [HP02] J.-S. Huang and P . Pand ˇzi´c. “Dirac cohomology, unitary repre- sentations and a proof of a conjecture of Vogan”. In: J. Amer. M...

work page 2011
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Families of symmetries and the hy- drogen atom

[HS22] N. Higson and E. Subag. “Families of symmetries and the hy- drogen atom”. In: Adv. Math. 408 (2022), Paper No. 108586,

work page 2022
[13]

Dirac cohomology of highest weight modules

[HX12] J.-S. Huang and W. Xiao. “Dirac cohomology of highest weight modules”. In: Selecta Math. (N.S.) 18.4 (2012), pp. 803–824. [IW53] E. Inonu and E. P . Wigner. “On the contraction of groups and their representations”. In: Proc. Nat. Acad. Sci. U.S.A. 39 (1953), pp. 510–524. [Jan25] F. Januszewski. “Families of D-Modules and Integral Models of (g, K)-M...

work page 2012
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On the analogy between semisimple Lie groups and certain related semi-direct product groups

Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1995, pp. xx+948. [Mac75] G. W. Mackey. “On the analogy between semisimple Lie groups and certain related semi-direct product groups”. In: Lie groups and their representations (Proc. Summer School, Bolyai J´ anos Math. Soc., Budapest,

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Computing the associated cycles of certain Harish-Chandra modules

Halsted Press, New York-Toronto, Ont., 1975, pp. 339–363. [Meh+18] S. Mehdi, P . Pand ˇzi´c, D. Vogan, and R. Zierau. “Computing the associated cycles of certain Harish-Chandra modules”. In: Glas. Mat., III. Ser. 53.2 (2018), pp. 275–330. [MP11] S. Mehdi and R. Parthasarathy. “Cubic Dirac cohomology for generalized Enright-Varadarajan modules”. In: J. Lie...

work page 1975
[16]

Dirac Operator and the Discrete Series

[Par72] R. Parthasarathy. “Dirac Operator and the Discrete Series”. In: Annals of Mathematics 96.1 (1972), pp. 1–30. [Par80] R. Parthasarathy. “Criteria for the unitarizability of some high- est weight modules”. In: Proc. Indian Acad. Sci., Math. Sci. 89 (1980), pp. 1–24. [PS16] P . Pand ˇzi´c and P . Somberg. “Higher Dirac cohomology of mod- ules with ge...

work page 1972
[17]

Strong contraction of the representations of the three-dimensional Lie algebras

[Sub+12] E. M. Subag, E. M. Baruch, J. L. Birman, and A. Mann. “Strong contraction of the representations of the three-dimensional Lie algebras”. In: J. Phys. A 45.26 (2012), pp. 265206,

work page 2012
[18]

Symmetries of the hydrogen atom and algebraic families

[Sub18] E. M. Subag. “Symmetries of the hydrogen atom and algebraic families”. In: J. Math. Phys. 59.7 (2018), pp. 071702,

work page 2018
[19]

The algebraic Mackey-Higson bijections

[Sub19] E. Subag. “The algebraic Mackey-Higson bijections”. In: J. Lie Theory 29.2 (2019), pp. 473–492. [Sub24] E. Subag. Extensions of the constant family of Harish-Chandra pairs of SL2(R)

work page 2019
[20]

Branching to a maximal compact subgroup

arXiv: 2411.00228 [math.RT]. [Vog07] D. A. Vogan Jr. “Branching to a maximal compact subgroup”. In: Harmonic analysis, group representations, automorphic forms and invariant theory . Vol

work page arXiv
[21]

Notes Ser

Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. World Sci. Publ., Hackensack, NJ, 2007, pp. 321–401. 60 [Vog97] D. A. Vogan. Dirac operator and unitary representations, 3 talks at MIT Lie groups seminar

work page 2007
[22]

The dependence on parameters of the inverse functor to the K-finite functor

[Wal22] N. R. Wallach. “The dependence on parameters of the inverse functor to the K-finite functor”. In: Represent. Theory 26 (2022), pp. 94–121. [Yu23] S. Yu. “Mackey analogy as deformation of D-modules”. In: Math. Ann. 385.1-2 (2023), pp. 421–457. Spyridon Afentoulidis-Almpanis DEPT. OF MATHEMATICS , BAR-ILAN UNIVERSITY , RAMAT-G AN, 5290002 I SRAEL E-...

work page 2022

[1] [1]

Unitary representations of real reductive groups

[Ada+20] J. D. Adams, M. A. A. van Leeuwen, P . E. Trapa, and D. A. Vogan Jr. “Unitary representations of real reductive groups”. In: Ast´ erisque417 (2020), pp. x +

work page 2020

[2] [2]

Dirac cohomology for the BGG cat- egory O

[Afe24] S. Afentoulidis-Almpanis. “Dirac cohomology for the BGG cat- egory O”. In: Indag. Math., New Ser. 35.2 (2024), pp. 205–229. [Afg20] A. Afgoustidis. “On the analogy between real reductive groups and Cartan motion groups: contraction of irreducible tempered representations”. In: Duke Math. J. 169.5 (2020), pp. 897–960. [Afg21] A. Afgoustidis. “On th...

work page 2024

[3] [3]

Algebraic families of Harish-Chandra pairs

[BHS20a] J. Bernstein, N. Higson, and E. Subag. “Algebraic families of Harish-Chandra pairs”. In:Int. Math. Res. Not. IMRN15 (2020), pp. 4776–4808. [BHS20b] J. Bernstein, N. Higson, and E. Subag. “Contractions of rep- resentations and algebraic families of Harish-Chandra mod- ules”. In: Int. Math. Res. Not. IMRN 11 (2020), pp. 3494–3520. [BP11] D. Barbasc...

work page 2020

[4] [4]

Dirac cohomology of unipotent representations of Sp(2n, R) and U(p, q)

Contemp. Math. Amer. Math. Soc., Providence, RI, 2011, pp. 1–22. [BP15] D. Barbasch and P . Pand ˇzi´c. “Dirac cohomology of unipotent representations of Sp(2n, R) and U(p, q)”. In: J. Lie Theory 25.1 (2015), pp. 185–213. [Cah13] B. Cahen. “A contraction of the principal series by Berezin- Weyl quantization”. In: Rocky Mountain J. Math. 43.2 (2013), pp. 4...

work page 2011

[5] [5]

[Cla+22] P

arXiv: 2202.02857 [math.RT]. [Cla+22] P . Clare, N. Higson, Y. Song, and X. Tang. On the Connes-Kasparov isomorphism, I: The reduced C*-algebra of a real reductive group and the K-theory of the tempered dual

work page arXiv

[6] [6]

Jacquet modules and Dirac coho- mology

arXiv: 2202.02855 [math.RT]. [DH11] C.-P . Dong and J.-S. Huang. “Jacquet modules and Dirac coho- mology”. In: Adv. Math. 226.4 (2011), pp. 2911–2934. [DR85] A. H. Dooley and J. W. Rice. “On contractions of semisimple Lie groups”. In: Trans. Amer. Math. Soc. 289.1 (1985), pp. 185–

work page arXiv 2011

[7] [7]

57 [Gil94] R. Gilmore. Lie groups, Lie algebras, and some of their applications. Reprint of the 1974 original. Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1994, pp. xx+587. [GW09] R. Goodman and N. R. Wallach. Symmetry, representations, and invariants. Vol

work page 1974

[8] [8]

Flat base change formulas for (g, K)-modules over Noetherian rings

Graduate Texts in Mathematics. Springer, Dordrecht, 2009, pp. xx+716. [Hay18] T. Hayashi. “Flat base change formulas for (g, K)-modules over Noetherian rings”. In: J. Algebra 514 (2018), pp. 40–75. [Hay19] T. Hayashi. “Dg analogues of the Zuckerman functors and the dual Zuckerman functors I”. In: J. Algebra 540 (2019), pp. 274–

work page 2009

[9] [9]

The Mackey analogy and K-theory

©2020, pp. 415–420. [Hig08] N. Higson. “The Mackey analogy and K-theory”. In: Group rep- resentations, ergodic theory, and mathematical physics: a tribute to George W. Mackey. Vol

work page 2020

[10] [10]

On the analogy between complex semisimple groups and their Cartan motion groups

Contemp. Math. Amer. Math. Soc., Providence, RI, 2008, pp. 149–172. [Hig11] N. Higson. “On the analogy between complex semisimple groups and their Cartan motion groups”. In:Noncommutative geometry and global analysis. Vol

work page 2008

[11] [11]

Dirac cohomology of some Harish-Chandra modules

Contemp. Math. Amer. Math. Soc., Providence, RI, 2011, pp. 137–170. [HKP09] J.-S. Huang, Yi-F. Kang, and P . Pand ˇzi´c. “Dirac cohomology of some Harish-Chandra modules”. In: Transform. Groups 14.1 (2009), pp. 163–173. [HP02] J.-S. Huang and P . Pand ˇzi´c. “Dirac cohomology, unitary repre- sentations and a proof of a conjecture of Vogan”. In: J. Amer. M...

work page 2011

[12] [12]

Families of symmetries and the hy- drogen atom

[HS22] N. Higson and E. Subag. “Families of symmetries and the hy- drogen atom”. In: Adv. Math. 408 (2022), Paper No. 108586,

work page 2022

[13] [13]

Dirac cohomology of highest weight modules

[HX12] J.-S. Huang and W. Xiao. “Dirac cohomology of highest weight modules”. In: Selecta Math. (N.S.) 18.4 (2012), pp. 803–824. [IW53] E. Inonu and E. P . Wigner. “On the contraction of groups and their representations”. In: Proc. Nat. Acad. Sci. U.S.A. 39 (1953), pp. 510–524. [Jan25] F. Januszewski. “Families of D-Modules and Integral Models of (g, K)-M...

work page 2012

[14] [14]

On the analogy between semisimple Lie groups and certain related semi-direct product groups

Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1995, pp. xx+948. [Mac75] G. W. Mackey. “On the analogy between semisimple Lie groups and certain related semi-direct product groups”. In: Lie groups and their representations (Proc. Summer School, Bolyai J´ anos Math. Soc., Budapest,

work page 1995

[15] [15]

Computing the associated cycles of certain Harish-Chandra modules

Halsted Press, New York-Toronto, Ont., 1975, pp. 339–363. [Meh+18] S. Mehdi, P . Pand ˇzi´c, D. Vogan, and R. Zierau. “Computing the associated cycles of certain Harish-Chandra modules”. In: Glas. Mat., III. Ser. 53.2 (2018), pp. 275–330. [MP11] S. Mehdi and R. Parthasarathy. “Cubic Dirac cohomology for generalized Enright-Varadarajan modules”. In: J. Lie...

work page 1975

[16] [16]

Dirac Operator and the Discrete Series

[Par72] R. Parthasarathy. “Dirac Operator and the Discrete Series”. In: Annals of Mathematics 96.1 (1972), pp. 1–30. [Par80] R. Parthasarathy. “Criteria for the unitarizability of some high- est weight modules”. In: Proc. Indian Acad. Sci., Math. Sci. 89 (1980), pp. 1–24. [PS16] P . Pand ˇzi´c and P . Somberg. “Higher Dirac cohomology of mod- ules with ge...

work page 1972

[17] [17]

Strong contraction of the representations of the three-dimensional Lie algebras

[Sub+12] E. M. Subag, E. M. Baruch, J. L. Birman, and A. Mann. “Strong contraction of the representations of the three-dimensional Lie algebras”. In: J. Phys. A 45.26 (2012), pp. 265206,

work page 2012

[18] [18]

Symmetries of the hydrogen atom and algebraic families

[Sub18] E. M. Subag. “Symmetries of the hydrogen atom and algebraic families”. In: J. Math. Phys. 59.7 (2018), pp. 071702,

work page 2018

[19] [19]

The algebraic Mackey-Higson bijections

[Sub19] E. Subag. “The algebraic Mackey-Higson bijections”. In: J. Lie Theory 29.2 (2019), pp. 473–492. [Sub24] E. Subag. Extensions of the constant family of Harish-Chandra pairs of SL2(R)

work page 2019

[20] [20]

Branching to a maximal compact subgroup

arXiv: 2411.00228 [math.RT]. [Vog07] D. A. Vogan Jr. “Branching to a maximal compact subgroup”. In: Harmonic analysis, group representations, automorphic forms and invariant theory . Vol

work page arXiv

[21] [21]

Notes Ser

Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. World Sci. Publ., Hackensack, NJ, 2007, pp. 321–401. 60 [Vog97] D. A. Vogan. Dirac operator and unitary representations, 3 talks at MIT Lie groups seminar

work page 2007

[22] [22]

The dependence on parameters of the inverse functor to the K-finite functor

[Wal22] N. R. Wallach. “The dependence on parameters of the inverse functor to the K-finite functor”. In: Represent. Theory 26 (2022), pp. 94–121. [Yu23] S. Yu. “Mackey analogy as deformation of D-modules”. In: Math. Ann. 385.1-2 (2023), pp. 421–457. Spyridon Afentoulidis-Almpanis DEPT. OF MATHEMATICS , BAR-ILAN UNIVERSITY , RAMAT-G AN, 5290002 I SRAEL E-...

work page 2022