| Abstract |
The Gaudin model was first introduced by Michel Gaudin to describe a completely integrable quantum spin chain. Since then, it has been reformulated using the machinery of vertex algebras and has garnered considerable attention. In this talk, I will describe the Gaudin models with irregular singularities for general linear Lie (super)algebras. My main goal is to establish a duality for the pair (g_1, g_2) in the models, where g_1 is any general linear Lie algebra, and g_2 is any general linear Lie superalgebra. The upshot is that the duality yields an equivalence between the actions of the Gaudin algebras with irregular singularities for g_1 and g_2 on a Fock space. I will also give an application and the classical version of the duality. This talk is based on joint work with Ngau Lam. |
