Representations of Lie Superalgebras in Prime Characteristic I

Abstract

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a mixture of p-power and 2-power divisibilities of dimensions of modules. We establish the Conjecture for basic classical Lie superalgebras.

v2, mild correction of typos, Proc. London Math. Soc. (to appear)

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