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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
  • Adriano Moura,
    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 Lie superalgebra, queer Lie superalgebra, loop superalgebra, equivariant map superalgebra, finite-dimensional representation, finite-dimensional module
MSC Classifications: 17B65, 17B10 show english descriptions Infinite-dimensional Lie (super)algebras [See also 22E65]
Representations, algebraic theory (weights)
17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65]
17B10 - Representations, algebraic theory (weights)
 

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