Affine and degenerate affine BMW algebras: Actions on tensor space

Daugherty, Zajj; Ram, Arun; Virk, Rahbar

doi:10.48550/arxiv.1205.1852

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2012

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“…We are grateful to Arun Ram for valuable discussions and for providing us with the preprints [2] and [3]. The second author would like to thank the School of Mathematics and Statistics of the University of Sydney for warm hospitality during her visit.…”

Section: Introductionmentioning

confidence: 99%

Characteristic maps for the Brauer algebra

Molev¹,

Rozhkovskaya²

2012

J Algebr Comb

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The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or symplectic group on a space of tensors, while the second is provided by the action of this group on the symmetric algebra of the corresponding Lie algebra. We consider the second characteristic map both in the orthogonal and symplectic case, and calculate the images of central idempotents of the Brauer algebra in terms of the Schur polynomials. The calculation is based on the Okounkov-Olshanski binomial formula for the classical Lie groups. We also reproduce the hook dimension formulas for representations of the classical groups by deriving them from the properties of the primitive idempotents of the symmetric group and the Brauer algebra.

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Section: Introductionmentioning

confidence: 99%