A modified Brauer algebra as centralizer algebra of the unitary group

Elduque, Alberto

doi:10.1090/S0002-9947-04-03602-5

A modified Brauer algebra as centralizer algebra of the unitary group
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by Alberto Elduque PDF

Trans. Amer. Math. Soc. 356 (2004), 3963-3983 Request permission

Abstract:

The centralizer algebra of the action of $U(n)$ on the real tensor powers $\otimes _\mathbb {R}^r V$ of its natural module, $V=\mathbb {C}^n$, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for $U(n)$ and with the decomposition of $\otimes _\mathbb {R}^r V$ into irreducible submodules is considered.

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