Capelli identities for Lie superalgebras

Details Capelli identities for Lie superalgebras Capelli identities for Lie superalgebras

1996-10-27

arxiv.org/abs/q-alg/9610032v1

Ann. Scient. Ec. Norm. Sup. 30 (1997), 847-872

Mathematics

Quantum Algebra

AMS-TeX 2.1, 24 pages

Scientific paper

We apply the technique of affine Hecke algebras to the invariant theory of the "queer" Lie superalgebra $q_N$. We give explicit formulas for the elements of a distinguished basis in the centre of $U(q_N)$, determined by "vanishing" conditions. We evaluate the corresponding differential operators on $C^{N|N}\otimes C^{M|M}$. In particular, we obtain an analogue for $q_N$ of the classical Capelli identity.

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