A duality of the twisted group algebra of the symmetric group and a Lie superalgebra

1998/11/13 by Manabu Yamaguchi, Yamaguchi, Manabu
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/9811090

AMS-TeX, 22 pages, submitted to Journal of Algebra

arxiv created 1998/11/27 · arxiv updated 2009/11/30

Abstract

Let A_k denote the twisted group algebra of the symmetric group S_k, whose representations correspond to the nonlinear projective representations of S_k. We establish a duality relation between A_k and a Lie superalgebra q(n), sometimes called the ``queer'' Lie superalgebra. This duality clarifies Schur's formula, in the sense that the Schur-Weyl duality clarifies Frobenius' formula.

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