Talk page
Title:
Reduction of cluster structure.
Speaker:
Abstract:
Given a surface and a Lie group, one can consider the quantized algebra of functions on the open locus of the corresponding moduli space of local systems, where all monodromies are in generic position. A cluster structure on the moduli space, allows one to endow the algebra with a family of canonical representations modelled on certain Schwartz spaces, as well as compatible actions of the mapping class group on the algebra and representations. A particular example of this construction yields quantum group, tensor products of its positive representations, and the action of the braid group by R-matrices. It turns out that considering non-generic monodromies allows one to access such algebras as DAHA and its spherical subalgebra on one hand, and finite-dimensional representations of the quantum group on the other. I will discuss how one can reduce generic monodromies to the non-generic ones, and what happens to the cluster structure in the process. The talk will be based on ongoing discussions and joint works, most of which are still in progress, with Mikhail Bershtein, Ivan Ip, Rinat Kedem, Philippe di Francesco, and Gus Schrader.
Link:
Workshop: