# Meeting Details

Title: Kazhdan-Lusztig parameters and extended quotients Algebra and Number Theory Seminar Roger Plymen, University of Manchester The Kazhdan-Lusztig triples $(s,u,\rho)$ parametrize irreducible representations of affine Hecke algebras (and certain irreducible representations of p-adic groups). The third term in the triple, namely $\rho$, is hard to compute. We show that the collection of all such triples has an unexpected geometric structure, namely an extended quotient, which is easy to compute. Each affine Hecke algebra contains a parameter q . We will delve into the role of this q , and see what happens when q = 1. The Springer correspondence (for irreducible representations of finite Weyl groups) plays a major role. This will be a non-technical talk. Joint work with Anne-Marie Aubert and Paul Baum.