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

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

1998-11-13

arxiv.org/abs/math/9811090v2

Mathematics

Representation Theory

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

Scientific paper

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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