Gram Determinants of TypeBn, Original Research Article

The Hecke algebra image = imageR, Q, q(Wn) over a commutative ringRwith the two parametersQ, qassociated with the Weyl groupWnof typeBnhas certain distinguished representations afforded by modulesimagelabelled by bipartitions λ ofn. These are precisely the irreducible image-modules, if image is semisimple. In general there is a symmetric image-invariant bilinear form defined onimage. We present here a formula for the determinant of the Gram matrix ofimage.