On Hecke algebras for $p$-adic groupsMPIM
by
MPIM, Vivatsgasse, 7 - Lecture Hall
Max Planck Institute for Mathematics
Oberseminar Arithmetic Geometry and Representation Theory
In this talk, I will present two results concerning the Hecke algebras for $p$-adic groups. First, I will discuss a result that, under mild tameness assumptions, every Bernstein block of a $p$-adic group $G$ is equivalent to a depth-zero Bernstein block of a twisted Levi subgroup of $G$. Moreover, these blocks are also equivalent to the category of modules over an extension of an affine Hecke algebra by a twisted group algebra. This result is the main result of my joint work with Jeffrey D. Adler, Jessica Fintzen, and Manish Mishra.
Next, I will explain a result that the affine Hecke algebra mentioned above is isomorphic to a unipotent Hecke algebra, whose $q$-parameters are explicitly computed by Lusztig.