Hecke Algebras and Simple Supercuspidal Representations
Moshe Adrian, University of Utah
A well known result of Borel says that category of modules over the Iwahori-Hecke algebra of a semisimple p-adic group G describes the Bernstein component associated to the unramified principal series of G. We consider Bernstein components associated to principal series induced from simple supercuspidal representations, recently discovered by Benedict Gross and Mark Reeder. We define and study Hecke algebras that describe these Bernstein components for Sp(2n) and G2. This is joint work with Gordan Savin.