AbstractIn this talk, I propose a class of eigenfunctions for the elliptic van Diejen operators (Ruijsenaars operators of type BC) which are represented by elliptic hypergeometric integrals of Selberg type. They are constructed from simple seed eigenfunctions by integral transformations, thanks to gauge symmetries and kernel function identities of the van Diejen operators. Based on a collaborat...
AbstractThere is a class of $\mathcal{U}_q(\widehat{sl}_2)$ models models where the infinite dimensional evaluation representations lead to Baxter's $TQ=Q+Q$ equation where $Q$ is an entire function rather than a polynomial. I will give a general introduction to the method of solving the Baxter equation in this case