Gram determinants of type B-n

[摘要] The Hecke algebra H=H-R,H-Q,H-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)over tilde (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)over tilde(lambda)>. We present here a formula for the determinant of the Gram matrix of <(S)over tild (lambda)>. (C) 1997 Academic Press.

[发布日期] 1997-03-15