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Equivariant Map Queer Lie Superalgebras

Published online by Cambridge University Press:  20 November 2018

Lucas Calixto
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859 e-mail:
Adriano Moura
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859 e-mail:
Alistair Savage
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON e-mail:
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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.

Research Article
Copyright © Canadian Mathematical Society 2016


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