Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie superalgebras

Details Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie superalgebras Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie superalgebras

2002-06-05

arxiv.org/abs/math/0206036v2

Advances in Mathematics 182 No. 1 (2004) 124-172

Mathematics

Representation Theory

47 pages, LaTeX format

Scientific paper

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 $\C^d\otimes\C^{m|n}$. 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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