We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.

Topics in the lectures: #1. Review of the LL (Local Langlands) conjecture. #2. Statement of the ABPS(Aubert-Baum-Plymen-Solleveld) conjecture. #3. Brief indication of the proof that for any connectedâ€¦ (More)

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 geometricallyâ€¦ (More)

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F). It takes the form of a bijection between, on the one hand, conjugacyâ€¦ (More)

In the representation theory of reductive p-adic groups G, the issue of reducibility of induced representations is an issue of great intricacy. It is our contention, expressed as a conjecture inâ€¦ (More)

We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal inductionâ€¦ (More)

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 chamberâ€¦ (More)

Recent work by a number of people has shown that complex reflection groups give rise to many representation-theoretic structures (e.g., generic degrees and families of characters), as though theyâ€¦ (More)

We obtain a formula for the values of the characteristic function of a character sheaf, in terms of the representation theory of certain finite groups related to the Weyl group. This formula, aâ€¦ (More)