Cyclotomic Gaudin models with irregular singularities

TL;DR

This paper introduces the universal cyclotomic Gaudin algebra, extending previous models to include irregular singularities, and solves a specific case using Bethe ansatz with particular pole configurations.

Contribution

It generalizes cyclotomic Gaudin models to irregular singularities and provides an explicit Bethe ansatz solution for a special pole configuration.

Findings

Construction of the universal cyclotomic Gaudin algebra.

Bethe ansatz solution for a specific pole configuration.

Extension of Gaudin models to 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.