Local Langlands Correspondence: From Extended Quotients to Affine Hecke Algebras

Explore a 57-minute conference talk from the Arithmetic Quantum Field Theory Conference where Anne-Marie Aubert from IMJ-PRG delves into the Local Langlands correspondence and its connections to extended quotients and affine Hecke algebras. Learn about the fundamental concept of extended quotients through practical examples and discover how they facilitate the construction of local Langlands correspondence in nonarchimedean cases. Understand the intricate relationship between extended quotients (connected to the Bernstein decomposition of smooth representations of p-adic groups), their Langlands duals, and representations of affine Hecke algebras, ultimately revealing how these elements combine to describe the Local Langlands Correspondence as a correspondence between categories of modules of two collections of such algebras.