Equivariant Map Queer Lie Superalgebras

Calixto, Lucas ; Moura, Adriano ; Savage, Alistair

Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 258-279

Résumé

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.

Détail

DOI : 10.4153/CJM-2015-033-6

Mots-clés : 17B65, 17B10, Lie superalgebra, queer Lie superalgebra, loop superalgebra, equivariant map superalgebra, finite-dimensional representation, finite-dimensional module