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Quantum Immanants and Higher Capelli Identities

Andrei Okounkov
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Abstract

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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Andrei Okounkov. 1996-02-19. Quantum Immanants and Higher Capelli Identities. https://arxiv.org/abs/q-alg/9602028

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