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Lie superalgebras, Clifford algebras, induced modules and nilpotent orbits

Authors
Journal
Advances in Mathematics
0001-8708
Publisher
Elsevier
Publication Date
Volume
207
Issue
1
Identifiers
DOI: 10.1016/j.aim.2005.03.016
Keywords
  • Lie Superalgebras
  • Induced Modules
  • Nilpotent Orbits
Disciplines
  • Mathematics

Abstract

Abstract Let g be a classical simple Lie superalgebra. To every nilpotent orbit O in g 0 we associate a Clifford algebra over the field of rational functions on O . We find the rank, k ( O ) of the bilinear form defining this Clifford algebra, and deduce a lower bound on the multiplicity of a U ( g ) -module with O or an orbital subvariety of O as associated variety. In some cases we obtain modules where the lower bound on multiplicity is attained using parabolic induction. The invariant k ( O ) is in many cases, equal to the odd dimension of the orbit G ⋅ O , where G is a Lie supergroup with Lie superalgebra g .

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