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Proceedings of the London Mathematical Society Advance Access originally published online on January 7, 2009
Proceedings of the London Mathematical Society 2009 99(1):145-167; doi:10.1112/plms/pdn057
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© 2009 London Mathematical Society

Representations of Lie superalgebras in prime characteristic I

Weiqiang Wang and Lei Zhao

Department of Mathematics
University of Virginia
Charlottesville
VA 22904 Virginia
USA
lz4u@virginia.edu

Received 4 August 2008.

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.

2000 Mathematics Subject Classification Primary 17B50.

This research is partially supported by NSA and NSF grants.


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