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A modified Brauer algebra as centralizer algebra of the unitary group

Author: Alberto Elduque
Journal: Trans. Amer. Math. Soc. 356 (2004), 3963-3983
MSC (2000): Primary 20G05, 17B10
Published electronically: May 10, 2004
MathSciNet review: 2058514
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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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Additional Information

Alberto Elduque
Affiliation: Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain

Keywords: Brauer algebra, unitary group, centralizer
Received by editor(s): June 9, 2003
Published electronically: May 10, 2004
Additional Notes: This research was supported by the Spanish Ministerio de Ciencia y Tecnología and FEDER (BFM 2001-3239-C03-03)
Article copyright: © Copyright 2004 American Mathematical Society