The Weil-Moore anima refines the Weil group into a space with higher homotopy groups to improve its cohomological behavior for number fields.
Relative Langlands Duality
8 Pith papers cite this work. Polarity classification is still indexing.
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2026 8verdicts
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Proves equivalence of categories for the S-dual of SO(2n)×Sp(2n) on C^{2n}⊗C^{2n} being SO(2n+1)×SO(2n) on T*SO(2n+1) as a non-polarized case of relative Langlands duality, with consequence for functoriality via theta correspondence.
New integral representation of the ∧² ⊗ std₂ L-function on GL₄ × GL₂ relating its central value to the generalized Shalika period, plus evidence for Gan-Gross-Prasad conjectures via theta correspondence.
Formulates almost multiplicity-one property for spherical G/H over F_q and establishes criterion in terms of B-stabilizers on G/H.
Defines equivalent P-monoids and L-monoids for S^2 bordisms in Cob(3) that add prime 3-manifold labeled endomorphisms or units to commutative Frobenius monoids, with legs relations forcing simplification to prime unit multiplications in algebras.
Assuming the Ben-Zvi-Sakellaridis-Venkatesh local conjecture and polarization, the authors deduce a Z/2-graded equivalence between B-equivariant D-modules on Y and unipotent B^vee-monodromic modules on the dual variety via S1-equivariant localization.
Functoriality of the local theta correspondence for classical p-adic groups is realized through adaptation of the Adams conjecture to ABV-packets, with evidence given particularly for general linear groups.
Sufficient conditions are given for Ginzburg-Rallis models of [2^3]-induced GL_6 representations to be isomorphic to trilinear models of the inducing data, with nonvanishing criteria.
citing papers explorer
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Weil-Moore anima
The Weil-Moore anima refines the Weil group into a space with higher homotopy groups to improve its cohomological behavior for number fields.
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Towards the Relative Langlands Duality for Orthosymplectic Pairs
Proves equivalence of categories for the S-dual of SO(2n)×Sp(2n) on C^{2n}⊗C^{2n} being SO(2n+1)×SO(2n) on T*SO(2n+1) as a non-polarized case of relative Langlands duality, with consequence for functoriality via theta correspondence.
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On Periods and $L$-functions for $\mathbf{GL}_4 \times \mathbf{GL}_2$
New integral representation of the ∧² ⊗ std₂ L-function on GL₄ × GL₂ relating its central value to the generalized Shalika period, plus evidence for Gan-Gross-Prasad conjectures via theta correspondence.
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Almost multiplicity-one property of spherical varieties over finite fields
Formulates almost multiplicity-one property for spherical G/H over F_q and establishes criterion in terms of B-stabilizers on G/H.
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Topological Field Theories and the Algebraic Structures of the Two-Sphere
Defines equivalent P-monoids and L-monoids for S^2 bordisms in Cob(3) that add prime 3-manifold labeled endomorphisms or units to commutative Frobenius monoids, with legs relations forcing simplification to prime unit multiplications in algebras.
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Relative Langlands duality and Koszul duality
Assuming the Ben-Zvi-Sakellaridis-Venkatesh local conjecture and polarization, the authors deduce a Z/2-graded equivalence between B-equivariant D-modules on Y and unipotent B^vee-monodromic modules on the dual variety via S1-equivariant localization.
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Functoriality and the theta correspondence
Functoriality of the local theta correspondence for classical p-adic groups is realized through adaptation of the Adams conjecture to ABV-packets, with evidence given particularly for general linear groups.
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On the trilinear and Ginzburg-Rallis models
Sufficient conditions are given for Ginzburg-Rallis models of [2^3]-induced GL_6 representations to be isomorphic to trilinear models of the inducing data, with nonvanishing criteria.