On representations of the Lie superalgebra p(n)

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 by the radical of U. We show that has a large center which separates typical finite-dimensional irreducible representations. We give a description of 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 in the coadjoint representation.