Duality for Knizhnik-Zamolodchikov and Dynamical Operators

Abstract

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.

References in corpus (3)

• The trigonometric Casimir connection of a simple Lie algebra
• $({\mathfrak{gl}}_M,{\mathfrak{gl}}_N)$-Dualities in Gaudin Models with Irregular Singularities
• The elliptic Casimir connection of a simple Lie algebra

Cited by in corpus (3)

• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Duality for Bethe algebras acting on polynomials in anticommuting variables
• Difference Operators and Duality for Trigonometric Gaudin and Dynamical Hamiltonians