Representations of Lie superalgebras in prime characteristic, III

Lei Zhao

Vol. 248 (2010), No. 2, 493–510

DOI: 10.2140/pjm.2010.248.493

Abstract

For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of g-modules. In particular, we give a new proof of the super Kac–Weisfeiler conjecture for basic classical Lie superalgebras. The new proof allows us to improve optimally the assumption on p. We also establish a semisimplicity criterion for the reduced enveloping superalgebras associated with semisimple p-characters for all basic classical Lie superalgebras using the technique of odd reflections.

Keywords

Lie superalgebras, modular representations

Mathematical Subject Classification 2000

Primary: 17B10, 17B50

Secondary: 17B20

Milestones

Received: 3 September 2009

Accepted: 10 November 2009

Published: 1 December 2010