Finite generation of Hochschild cohomology of Hecke algebras of finite classical type in characteristic zero

Abstract

We show that the Hochschild cohomology HH*(ℋ) of a Hecke algebra ℋ of finite classical type over a field k of characteristic zero and a non-zero parameter q in k is finitely generated, unless possibly if q has even order in k× and ℋ is of type B or D