On representations of the Lie superalgebra p(n)

By Vera Serganova. 2002

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Abstract We introduce a new way to study representations of the Lie superalgebra p(n). Since the center of the universal enveloping algebra U acts trivially on all irreducible representations, we suggest to study the quotient algebra U by the radical of U. We show that U has a large center which separates typical finite-dimensional irreducible representations. We give a description of U factored by a generic central character. Using this description we obtain character formulae of generic (infinite-dimensional) irreducible representations. We also describe some geometric properties of the supervariety Spec Gr U in the coadjoint representation.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72062de4def525a33596a4a7737fb87b9372de28