Strongly typical representations of the basic classical Lie superalgebras

By M. Gorelik. 2000

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1.1. In [PS1], I. Penkov and V. Serganova show that the category of representations of a basic classical Lie superalgebra g of type I with a fixed typical central character is equivalent to the category of representations of the even part go with a suitable central character. A similar result for type II was proven by I. Penkov in [P] for "generic" central characters. The aim of this paper is to understand for which central characters such an equivalence holds. We also study a simplest example when such an equivalence fails to exist, but the corresponding category of representations of a Lie superalgebra still has a good description.

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

View Paper: https://www.semanticscholar.org/paper/ce9c12c410c06580af2d134eb5b121606bc56bb5