Gram Determinants of Type B_n

Richard Dipper, Gordon James and Eugene Murphy

Keywords

Hecke algebras, Gram determinants. 

Status

To appear.

Abstract

The Hecke algebra H = H_{R,Q,q}(W_n) over a commutative ring R with the two 
parameters Q,q associated with the Weyl group W_n of type B_n has certain
distinguished representations afforded by modules S^{\lambda} labelled by 
bipartitions \lambda of n. These are precisely the irreducible H-modules, 
if H is semisimple. In general there is a symmetric H-invariant bilinear form 
defined on S^\lambda. We present here a formula for the determinant of the 
Gram matrix of S^\lambda.