# Projection Maps for Tensor Products of <i>gl</i>(<i>r, C</i>)-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 *T* =*V*(*λ_1)⊗ ⋯ ⊗_T* =*V*(*λm*) of the finite dimensional irreducible *G* = *gl*(*r, C*) modules labelled by partitions _λ_1,⋯,*λm* of *m* not necessarily distinct numbers _n_1,⋯,*nm* respectively. We determine the centralizer algebra *EndG*(*T*) and the projection maps of *T* onto its irreducible *G*-summands and give an explicit construction of the corresponding maximal vectors. In the special case that *ni* = 1 for *i* = 1,⋯,*m*, 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 <i>gl</i>(<i>r, C</i>)-Representations. Publ. Res. Inst. Math. Sci. 28 (1992), no. 6, pp. 983–1010

DOI 10.2977/PRIMS/1195167734