Structure of a Hecke algebra quotient

Abstract

Let W W be a Coxeter group with Coxeter graph γ \gamma . Let H \mathcal {H} be the associated Hecke algebra. We define a certain ideal I \mathcal {I} in H \mathcal {H} and study the quotient algebra H ¯ = H / I \bar {\mathcal {H}} = \mathcal {H}/\mathcal {I} . We show that when γ \gamma is one of the infinite series of graphs of type E E , the quotient is semi-simple. We examine the cell structures of these algebras and construct their irreducible representations. We discuss the case where γ \gamma is of type B B , F F , or H H .