## Abstract

For the complex general linear group G = GL(r, C) we investigate the tensor product module T= (⨂^{p} V)⨂(⨂^{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 퓎 of all transformations on T commuting with the action of G, to construct the irreducible C-representations, and to identify 퓎 with a certain subalgebra ⨂^{(r)} _{p, q} of the Brauer algebra ⨂^{(r)}_{p+q}.

Original language | English (US) |
---|---|

Pages (from-to) | 529-567 |

Number of pages | 39 |

Journal | Journal of Algebra |

Volume | 166 |

Issue number | 3 |

DOIs | |

State | Published - Jun 15 1994 |