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Proceedings of the London Mathematical Society Advance Access originally published online on October 17, 2007
Proceedings of the London Mathematical Society 2008 96(1):251-271; doi:10.1112/plms/pdm040
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© 2007 London Mathematical Society

Modular representations of the ortho-symplectic supergroups

Bin Shu

Department of Mathematics
East China Normal University
Shanghai 200062
China

Weiqiang Wang

Department of Mathematics
University of Virginia
Charlottesville
VA 22904
USA
ww9c@virginia.edu

Received 29 November 2006. Revision received 10 August 2007.

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where a key combinatorial component comes from the Mullineux conjecture on modular representations of the symmetric group. A Steinberg tensor product theorem for the ortho-symplectic supergroup is also obtained.

2000 Mathematics Subject Classification 20G05 (primary) 17B50, 05E10 (secondary).


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