Projection Maps for Tensor Products of -Representations

  • Georgia Benkart

    University of Wisconsin, Madison, USA
  • Daniel Britten

    University of Windsor, Windsor, Canada
  • Frank Lemire

    University of Windsor, Windsor, Canada

Abstract

We investigate the tensor product of the finite dimensional irreducible modules labelled by partitions of not necessarily distinct numbers respectively. We determine the centralizer algebra and the projection maps of onto its irreducible -summands and give an explicit construction of the corresponding maximal vectors. In the special case that for , the results reduce to the well-known results of Schur and Weyl.

Cite this article

Georgia Benkart, Daniel Britten, Frank Lemire, Projection Maps for Tensor Products of -Representations. Publ. Res. Inst. Math. Sci. 28 (1992), no. 6, pp. 983–1010

DOI 10.2977/PRIMS/1195167734