Celebratio Mathematica — Benkart

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G. Benkart, M. Chakrabarti, T. Halverson, R. Leduc, C. Lee, and J. Stroomer: “Tensor product representations of general linear groups and their connections with Brauer algebras,” J. Algebra 166 : 3 (June 1994), pp. 529–567. For J. Marshall Osborn and Louis Solomon on their 60th birthdays. MR 1280591 Zbl 0815.20028 article

For the complex general linear group \( G = GL(r,\mathbb{C}) \) we investigate the tensor product module \[\textstyle T = (\bigotimes^p V)\otimes(\bigotimes^q V^*) \] of \( p \) copies of its natural representation \( V = \mathbb{C}^r \) and \( q \) copies of the dual space \( V^* \) 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 \( \mathscr{C} \) of all transformations on \( T \) commuting with the action of \( G \), to construct the irreducible \( \mathscr{C} \)-representations, and to identify \( \mathscr{C} \) with a certain subalgebra \( \mathscr{B}^{(r)}_{p,q} \) of the Brauer algebra \( \mathscr{B}(r)_{p+q} \).

Jeffrey D. Stroomer	Related
Thomas Michael Halverson	Related
Louis Solomon	Related
Robert Edgar Leduc	Related
Chanyoung Lee Shader	Related
Manish Chakrabarti	Related
J. Marshall Osborn	Related