Howe Duality and Combinatorial Character Formula for Orthosymplectic Lie Superalgebras
نویسندگان
چکیده
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 ⊗ C. 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.
منابع مشابه
Supplement to Orthosymplectic Lie Superalgebras, Koszul Duality, and a Complete Intersection Analogue of the Eagon–northcott Complex
This note is a supplement to [S2]. The main point is to prove Theorem 2.1.1, which is a special case of [S2, Theorem 3.3.6], without the use of Lie superalgebras or Koszul duality. The focus here is on the case of the symplectic group, though the proofs given here could be adapted to the other cases from [S2]. The proof we give here was found before the one in [S2] and we believe that it is of ...
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