On representations of the Lie superalgebra p(n)

[摘要] 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) over bar by the radical of U. We show that (U) over bar has a large center which separates typical finite-dimensional irreducible representations. We give a description of (U) over bar 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) over bar in the coadjoint representation. (C) 2002 Elsevier Science (USA). All rights reserved.

[发布日期] 2002-12-15