Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
and Shalika, Joseph A
6 Pith papers cite this work. Polarity classification is still indexing.
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Formulates a conjectural classification of H_{1,n-1}-distinguished irreducible smooth representations of GL_n(D) for n>2 and proves it for n=3 and n=4.
Geometrizes Poisson summation for quadrics over number fields by relating Braverman-Kazhdan and theta-lift Schwartz spaces.
Proves unconditional effective joint Sato-Tate distribution for coefficients of two twist-inequivalent non-CM newforms, generalizing to measurable subsets with finite-length curve boundaries and yielding sign-change results for symmetric powers.
Studies differential operators on Braverman-Kazhdan spaces P^der backslash G and claims they share structural properties with Weyl algebras while developing D-module theory.
A survey paper presents the Geometric Langlands correspondence informally as an algebraic spectral theorem for automorphic sheaves and a blueprint for studying nonabelian symmetry.
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Quasi-Classical Braverman--Kazhdan Intertwiners via Quiver Varieties
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
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On representations of GL(n) distinguished by GL(1)*GL(n-1) over a quaternion division algebra
Formulates a conjectural classification of H_{1,n-1}-distinguished irreducible smooth representations of GL_n(D) for n>2 and proves it for n=3 and n=4.
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Weyl algebras on Braverman-Kazhdan spaces
Studies differential operators on Braverman-Kazhdan spaces P^der backslash G and claims they share structural properties with Weyl algebras while developing D-module theory.
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What is the Geometric Langlands Correspondence about?
A survey paper presents the Geometric Langlands correspondence informally as an algebraic spectral theorem for automorphic sheaves and a blueprint for studying nonabelian symmetry.