Abstract view
Equivariant Map Queer Lie Superalgebras


Published:20150915
Printed: Apr 2016
Lucas Calixto,
UNICAMP  IMECC, Campinas  SP  Brazil, 13083859
Adriano Moura,
UNICAMP  IMECC, Campinas  SP  Brazil, 13083859
Alistair Savage,
Department of Mathematics and Statistics, University of Ottawa, Canada
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 finitedimensional
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 finitedimensional
representations of $\mathfrak{q}$. In the special case where $X$ is the
torus, we obtain a classification of the irreducible finitedimensional
representations of the twisted loop queer superalgebra.
Keywords: 
Lie superalgebra, queer Lie superalgebra, loop superalgebra, equivariant map superalgebra, finitedimensional representation, finitedimensional module
Lie superalgebra, queer Lie superalgebra, loop superalgebra, equivariant map superalgebra, finitedimensional representation, finitedimensional module
