TENSOR PRODUCT REPRESENTATIONS OF GENERAL LINEAR-GROUPS AND THEIR CONNECTIONS WITH BRAUER ALGEBRAS

[摘要] For the complex general linear group G = GL(r, C) we investigate the tensor product module T= (x p V)x(x q V) of p copies of its natural representation V = C(r) and q copies of the dual spare V of V. We describe the maximal vectors of T and from that obtain an explicit decomposition of T into its irreducible G-summands. Knowledge of the maximal vectors allows us to determine the centralizer algebra C of all transformations on T commuting with the action of G, to construct the irreducible C-representations, and to identify C with a certain subalgebra B(p,q)(r) of the Brauer algebra B(p+q)(r). (C) 1994 Academic Press, Inc.

[发布日期] 1994-06-15