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(glM,glN)-Dualities in Gaudin Models with Irregular Singularities

2018
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Symmetry, Integrability and Geometry: Methods and Applications
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We establish $({\mathfrak{gl}}_M, {\mathfrak{gl}}_N)$-dualities between quantum Gaudin models with irregular singularities. Specifically, for any $M, N \in {\mathbb Z}_{\geq 1}$ we consider two Gaudin models: the one associated with the Lie algebra ${\mathfrak{gl}}_M$ which has a double pole at infinity and $N$ poles, counting multiplicities, in the complex plane, and the same model but with the roles of $M$ and $N$ interchanged. Both models can be realized in terms of Weyl algebras, i.e., free

doi:10.3842/sigma.2018.040
fatcat:3zj5ibjalfagle56ug2ouhpjrm