Abstracts

Igor Salom

Generalized sl(2) Gaudin algebra and corresponding Knizhnik-Zamolodchikov equation

The Gaudin model has been revisited many times, yet some important issues remained open. In this talk, I will present our recent results on this topic. In particular, I will discuss the relationship between the off-shell Bethe vectors and the solutions of the corresponding Knizhnik-Zamolodchikov equations for the non-periodic sl(2) Gaudin model. Next, I will derive the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, I will also provide a closed-form expression for the scalar products of the off-shell Bethe vectors. Finally, I will demonstrate an explicit closed-form of the off-shell Bethe vectors, together with a sketch of a proof of implementation of the algebraic Bethe ansatz in full generality.