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

Manabu Yamaguchi
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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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Manabu Yamaguchi. 1998-11-27. A duality of the twisted group algebra of the symmetric group and a Lie superalgebra. https://arxiv.org/abs/math/9811090

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