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A reverse engineering approach to the Weil representation
We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put themExpand
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The local Langlands correspondence for inner forms of SL$$_{n}$$n
Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $$\mathrm{SL}_n (F)$$SLn(F). It takes the form of a bijection between, on theExpand
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Character sheaves and generalized Springer correspondence
  • A. Aubert
  • Mathematics
  • Nagoya Mathematical Journal
  • 2003
Abstract Let G be a connected reductive algebraic group over an algebraic closure of a finite field of characteristic p. Under the assumption that p is good for G, we prove that for each characterExpand
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Springer Correspondences for Dihedral Groups
Recent work by a number of people has shown that complex reection groups give rise to many representation-theoretic structures (e.g., generic degrees and families of characters), as though they wereExpand
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Geometric structure in the representation theory of p-adic groups
This expository note will state the ABP (Aubert-Baum-Plymen) conjecture. The conjecture can be stated at four levels: 1. K-theory of C*-algebras 2. Periodic cyclic homology of finite type algebras 3.Expand
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Cycles in the chamber homology of GL(3)
Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the existence of parahoric types for GL(N). We construct representative cycles in all the homology classes of the chamberExpand
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Plancherel measure for and : Explicit formulas and Bernstein decomposition
Let F be a nonarchimedean local field, let GL(n) = GL(n, F ) and let ν denote Plancherel measure for GL(n). Let Ω be a component in the Bernstein variety Ω(GL(n)). Then Ω yields its fundamentalExpand
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The Hecke algebra of a reductive p-adic group: a view from noncommutative geometry
Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometricallyExpand
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Kazhdan-Lusztig parameters and extended quotients
The Kazhdan-Lusztig parameters are important parameters in the representation theory of $p$-adic groups and affine Hecke algebras. We show that the Kazhdan-Lusztig parameters have a definiteExpand
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Conjectures about p-adic groups and their noncommutative geometry
Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statementsExpand
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