Structure of a Hecke algebra quotient

Structure of a Hecke Algebra Quotient

Let W be a Coxeter group with Coxeter graph Γ. Let H be theassociated Hecke algebra. We define a certain ideal I in H and study thequotient algebra H̄ = H/I. We show that when Γ is one of the infinite seriesof graphs of type E, the quotient is semi-simple. We examine the cell structuresof these algebras and construct their irreducible representations. We discussthe case where...

A Hecke Algebra Quotient and Some Combinatorial Applications

Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient H of H and show that it has a basis parametrized by a certain subset Wc of the Coxeter group w. Specifically, Wc consists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommu...

Structure coefficients of the Hecke algebra of (S2n,Bn)

The Hecke algebra of the pair (S2n,Bn), where Bn is the hyperoctahedral subgroup of S2n, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial universal algebra which projects on the Hecke algebra of (S2n,Bn) for every n. To build it, ...

The affine Hecke algebra

1 The affine Hecke algebra 1.1 The alcove walk algebra Fix notations for the Weyl group W , the extended affine Weyl group W , and their action on Ω × h * R as in Section 2. Label the walls of the alcoves so that the fundamental alcove has walls labeled 0, 1,. .. , n and the labeling is W-equivariant (see the picture in (2.12)). The periodic orientation is the orientation of the walls of the al...

Hecke Algebra Characters