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

Abstract

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.

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

References in corpus (2)

• Regular strongly typical blocks of ${\mathcal{O}}^{\mathfrak{q}}$
• Finite $W$-superalgebras for queer Lie superalgebras

Cited by in corpus (4)

• Nilpotent orbits and finite W-algebras
• Ambidextrous objects and trace functions for nonsemisimple categories
• Support varieties and representations of tame basic classical Lie superalgebras
• Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras