Frobenius-like structure in Gaudin model

Abstract

We introduce a Frobenius-like structure for the ${\mathfrak{sl}}_2$ Gaudin model. Namely, we introduce potential functions of the first and second kind. We describe the Shapovalov form in terms of derivatives of the potential of the first kind and the action of Gaudin Hamiltonians in terms of derivatives of the potential of the second kind.

Latex, 14 pages