Quantum Immanants and Higher Capelli Identities

Details Quantum Immanants and Higher Capelli Identities Quantum Immanants and Higher Capelli Identities

1996-02-19

arxiv.org/abs/q-alg/9602028v1

Transformation Groups, 1 (1996), 99--126

Mathematics

Quantum Algebra

Scientific paper

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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