Representations of Lie superalgebras in prime characteristic II: The queer series

Details Representations of Lie superalgebras in prime characteristic II: The queer series Representations of Lie superalgebras in prime characteristic II: The queer series

2009-02-16

arxiv.org/abs/0902.2758v4

J. Pure and Applied Alg. 215 (2011), 2515--2532

Mathematics

Representation Theory

26 pages, 2 diagrams and 4 tables, v4, to appear in J. Pure App. Algebra

Scientific paper

The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters and a criterion for the semisimplicity of the corresponding reduced enveloping algebras. A (2p)-power divisibility of dimensions of q(n)-modules with nilpotent p-characters is established. The representation theory of q(2) is treated in detail. We formulate a Morita super-equivalence conjecture for q(n) with general p-characters which is verified for n=2.

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