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arxiv: q-alg/9602028 · v1 · submitted 1996-02-19 · q-alg · math.QA

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Quantum Immanants and Higher Capelli Identities

Andrei Okounkov

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classification q-alg math.QA
keywords immanantsquantumalgebracapelliidentitiescallcentralclassical
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We consider remarkable central elements of the universal enveloping algebra of the general linear algebra which we call quantum immanants. We express them in terms of generators $E_{ij}$ and as differential operators on the space of matrices. These expressions are a direct generalization of the classical Capelli identities. They result in many nontrivial properties of quantum immanants.

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