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Duality for Knizhnik-Zamolodchikov and dynamical operators. (English) Zbl 1487.17035

Summary: We consider the Knizhnik-Zamolodchikov and dynamical operators, both differential and difference, in the context of the \((\mathfrak{gl}_k, \mathfrak{gl}_n)\)-duality for the space of polynomials in \(kn\) anticommuting variables. We show that the Knizhnik-Zamolodchikov and dynamical operators naturally exchange under the duality.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
39A12 Discrete version of topics in analysis
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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References:

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