Abstract
The centralizer algebra of the action of U ( n ) U(n) on the real tensor powers ⊗ R r V \otimes _\mathbb {R}^r V of its natural module, V = C n 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 ) U(n) and with the decomposition of ⊗ R r V \otimes _\mathbb {R}^r V into irreducible submodules is considered.
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