Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie superalgebras

2002/06/30 by Shun-Jen Cheng, R. B. Zhang · 1 citation
Mathematics · #math.RT #math.QA #msc:17B67

paper · pdf

published as Advances in Mathematics 182 No. 1 (2004) 124-172 · 47 pages, LaTeX format

arxiv created 2003/01/17 · arxiv updated 2009/11/30

Abstract

We study the Howe dualities involving the reductive dual pairs (O(d),spo(2m|2n)) and (Sp(d),osp(2m|2n)) on the (super)symmetric tensor of \C^d⊗\C^m|n. We obtain complete decompositions of this space with respect to their respective joint actions. We also use these dualities to derive a character formula for these irreducible representations of spo(2m|2n) and osp(2m|2n) that appear in these decompositions.

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