Search Results - "Kazhdan, David"
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Quantization of Lie Bialgebras, Part VI: Quantization of Generalized Kac–Moody Algebras
Published in Transformation groups (01-12-2008)“…This paper is a continuation of the series of papers “ Quantization of Lie bialgebras (QLB) I-V”. We show that the image of a Kac-Moody Lie bialgebra with the…”
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Differential operators on G/U and the Gelfand-Graev action
Published in Advances in mathematics (New York. 1965) (16-07-2022)“…Let G be a complex semisimple group and U its maximal unipotent subgroup. We study the algebra D(G/U) of algebraic differential operators on G/U and also its…”
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Schmidt rank of quartics over perfect fields
Published in Israel journal of mathematics (01-06-2023)“…Let k be a perfect field of characteristic ≠ 2. We prove that the Schmidt rank (also known as strength) of a quartic polynomial f over k is bounded above in…”
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Properties of High Rank Subvarieties of Affine Spaces
Published in Geometric and functional analysis (01-08-2020)“…We use tools of additive combinatorics for the study of subvarieties defined by high rank families of polynomials in high dimensional F q -vector spaces. In…”
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A construction of projective bases for irreducible representations of multiplicative groups of division algebras over local fields
Published in Selecta mathematica (Basel, Switzerland) (01-10-2019)“…Let F 0 be a local non-archimedian field of positive characteristic, D 0 a skew-field with center F 0 and G 0 : = D 0 × the multiplicative group of D 0 . The…”
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Correction to: Acknowledgments in six articles published in Selecta Mathematica
Published in Selecta mathematica (Basel, Switzerland) (2019)“…Papers [1–6] have received funding from ERC under Grant Agreement No. 669655…”
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Hecke operators and analytic Langlands correspondence for curves over local fields
Published in Duke mathematical journal (15-08-2023)Get full text
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A spectral decomposition of orbital integrals for PGL(2, F) (with an appendix by S. Debacker)
Published in Selecta mathematica (Basel, Switzerland) (01-03-2018)“…Let F be a local non-archimedian field, G a semisimple F -group, dg a Haar measure on G and S ( G ) be the space of locally constant complex valued functions f…”
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Applications of Algebraic Combinatorics to Algebraic Geometry
Published in Indagationes mathematicae (01-12-2021)“…We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics…”
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Perverse sheaves on infinite-dimensional stacks, and affine Springer theory
Published in Advances in mathematics (New York. 1965) (29-10-2022)Get full text
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On Ranks of Polynomials
Published in Algebras and representation theory (01-10-2018)“…Let V be a vector space over a field k , P : V → k , d ≥ 3. We show the existence of a function C ( r , d ) such that r a n k ( P ) ≤ C ( r , d ) for any field…”
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On Shalika germs
Published in Selecta mathematica (Basel, Switzerland) (01-10-2016)“…Let G be (the group of F -points of) a reductive group over a local field F satisfying the assumptions of Debacker (Ann Sci Ecole Norm Sup 35(4):391–422, 2002…”
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Polynomial functions as splines
Published in Selecta mathematica (Basel, Switzerland) (01-06-2019)“…Let V be a vector space over a finite field k . We give a condition on a subset A ⊂ V that allows for a local criterion for checking when a function f : A → k…”
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Approximate cohomology
Published in Selecta mathematica (Basel, Switzerland) (01-03-2018)“…Let k be a field, G be an abelian group and r ∈ N . Let L be an infinite dimensional k -vector space. For any m ∈ End k ( L ) we denote by r ( m ) ∈ [ 0 , ∞ ]…”
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Divergent Integrals, Residues of Dolbeault Forms, and Asymptotic Riemann Mappings
Published in International mathematics research notices (01-10-2017)“…Abstract We describe the asymptotic behaviour and the dependence on the regularization of logarithmically divergent integrals of products of meromorphic and…”
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Isoperimetric Inequalities for Ramanujan Complexes and Topological Expanders
Published in Geometric and functional analysis (01-02-2016)“…Expander graphs have been intensively studied in the last four decades (Hoory et al., Bull Am Math Soc, 43(4):439–562, 2006 ; Lubotzky, Bull Am Math Soc,…”
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Representations of algebraic groups over a 2-dimensional local field
Published in Geometric and functional analysis (01-06-2004)Get full text
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Regularization of divergent integrals
Published in Selecta mathematica (Basel, Switzerland) (01-03-2018)“…We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the…”
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The spherical Hecke algebra for affine Kac-Moody groups I
Published in Annals of mathematics (01-11-2011)“…We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake…”
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Analytic Langlands correspondence for $$PGL_2$$ on $${\mathbb {P}}^1$$ with parabolic structures over local fields
Published in Geometric and functional analysis (18-05-2022)“…Abstract We continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of…”
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