# Cyclotomic Gaudin models and hyperplane arrangements.

### Charles Young (University of Hertfordshire)

Thursday 19th November, 2015 16:00-17:00 Maths 522

#### Abstract

Given a simple Lie algebra g and an automorphism of g, I will define a cyclotomic Gaudin algebra. This is a large commutative subalgebra of U(g)^{\otimes N} generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case of the identity automorphism. I will go on to discuss the solution of this model, for a spin chain consisting of a tensor product of Verma modules, by generalizing an approach to the Bethe ansatz, due to Feigin, Frenkel and Reshetikhin, involving vertex algebras, coinvariants, and the Wakimoto construction. This is joint work Benoit Vicedo; see http://arxiv.org/abs/1409.6937.

If time permits I will discuss some related work in progress, joint with A. Varchenko, on hyperplane arrangements with cyclotomic symmetry,