1 5 A ug 2 00 0 REMARKS ON THE SCHUR – HOWE – SERGEEV DUALITY
نویسنده
چکیده
We establish a new Howe duality between a pair of two queer Lie superalgebras (q(m), q(n)). This gives a representation theoretic interpretation of a well-known combinatorial identity for Schur Q-functions. We further establish the equivalence between this new Howe duality and the Schur–Sergeev duality between q(n) and a central extension H̃k of the hyperoctahedral group Hk. We show that the zero-weight space of a q(n)-module with highest weight λ given by a strict partition of n is an irreducible module over the finite group H̃n parameterized by λ. We also discuss some consequences of this Howe duality. Mathematics Subject Classifications (2000): 17B67.
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