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Equivariant Map Queer Lie Superalgebras

Published online by Cambridge University Press:  20 November 2018

Lucas Calixto ,
Adriano Moura  and
Alistair Savage
Lucas Calixto
Affiliation:
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859 e-mail: lhcalixto@ime.unicamp.br aamoura@ime.unicamp.br
Adriano Moura
Affiliation:
UNICAMP - IMECC, Campinas - SP - Brazil, 13083-859 e-mail: lhcalixto@ime.unicamp.br aamoura@ime.unicamp.br
Alistair Savage
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON e-mail: alistair.savage@uottawa.ca
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Abstract

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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.

Keywords

17B6517B10Lie superalgebraqueer Lie superalgebraloop superalgebraequivariant map superalgebrafinite-dimensional representationfinite-dimensional module
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 2 , 01 April 2016 , pp. 258 - 279
Copyright
Copyright © Canadian Mathematical Society 2016

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