Cyclotomic Gaudin models with irregular singularities

Abstract

Generalizing the construction of the cyclotomic Gaudin algebra from arXiv:1409.6937, we define the universal cyclotomic Gaudin algebra. It is a cyclotomic generalization of the Gaudin models with irregular singularities defined in arXiv:math/0612798. We go on to solve, by Bethe ansatz, the special case in which the Lax matrix has simple poles at the origin and arbitrarily many finite points, and a double pole at infinity.

39 pages

References in corpus (5)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• Quantization of the Gaudin System
• On higher order Sugawara operators
• Quantization of soliton systems and Langlands duality
• Integrable Models From Twisted Half Loop Algebras

Cited by in corpus (4)

• 3-dimensional mixed BF theory and Hitchin's integrable system
• $({\mathfrak{gl}}_M,{\mathfrak{gl}}_N)$-Dualities in Gaudin Models with Irregular Singularities
• Affine opers and conformal affine Toda
• Lagrangian Multiform for Cyclotomic Gaudin Models