A duality of the twisted group algebra of the symmetric group and a Lie superalgebra
Manabu Yamaguchi
Abstract
Let Ak denote the twisted group algebra of the symmetric group Sk, whose representations correspond to the nonlinear projective representations of Sk. We establish a duality relation between Ak 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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