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# Equivariant Map Queer Lie Superalgebras

Published:2015-09-15
Printed: Apr 2016
• Lucas Calixto,
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859
• Alistair Savage,
Department of Mathematics and Statistics, University of Ottawa, Canada
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## Abstract

An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra $\mathfrak{q}$ that are equivariant with respect to the action of a finite group $\Gamma$ acting on $X$ and $\mathfrak{q}$. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that $\Gamma$ is abelian and acts freely on $X$. We show that such representations are parameterized by a certain set of $\Gamma$-equivariant finitely supported maps from $X$ to the set of isomorphism classes of irreducible finite-dimensional representations of $\mathfrak{q}$. In the special case where $X$ is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.
 Keywords: Lie superalgebra, queer Lie superalgebra, loop superalgebra, equivariant map superalgebra, finite-dimensional representation, finite-dimensional module
 MSC Classifications: 17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65] 17B10 - Representations, algebraic theory (weights)

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