On representations of the Lie superalgebra p(n)

Author: Serganova V.

Source: Journal of Algebra, Volume 258, Number 2, December 2002 , pp. 615-630(16)

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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\overline{{U}}by the radical of U. We show that\overline{{U}}has a large center which separates typical finite-dimensional irreducible representations. We give a description of\overline{{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\mathrm{{Spec\hspace{0.2em}Gr}}\overline{{U}}in the coadjoint representation.

Language: English

Document Type: Research article

DOI: http://dx.doi.org/10.1016/S0021-8693(02)00645-2

Publication date: 2002-12-01