Hecke algebras of classical type and their representation type

Abstract

The purpose of this article is to determine the representation type for all of the Hecke algebras of classical type. To do this, we combine methods from our previous work, which is used to obtain information on their Gabriel quivers, and recent advances in the theory of finite-dimensional algebras. The principal computation is for Hecke algebras of type B with two parameters. Then, we show that the representation type of Hecke algebras is governed by their Poincare polynomials.