On representations of the Lie superalgebra p(n)

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 $\bar{U}$ by the radical of $U$. We show that $\bar{U}$ has a large center which separates typical finite dimensional irreducible representations. We give a description of $\bar{U}$ 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 $Spec Gr \bar{U}$ in the coadjoint representation.