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Publications Influence

A reverse engineering approach to the Weil representation

- A. Aubert, T. Przebinda
- Mathematics
- 21 June 2014

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 them… Expand

16 3- PDF

The local Langlands correspondence for inner forms of SL$$_{n}$$n

- A. Aubert, P. Baum, R. Plymen, M. Solleveld
- Mathematics
- 1 May 2013

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 the… Expand

37 1- PDF

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 character… Expand

7 1- PDF

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 were… Expand

5 1- PDF

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

18 1- PDF

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 chamber… Expand

5 1- PDF

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 fundamental… Expand

1 1

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 geometrically… Expand

11 1

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 definite… Expand

2 1- PDF

Conjectures about p-adic groups and their noncommutative geometry

- A. Aubert, P. Baum, R. Plymen, M. Solleveld
- Mathematics
- 12 August 2015

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 statements… Expand

22 1- PDF

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