Abstract

The collection of Bethe subalgebras forms a flat family of maximal commutative subalgebras of the Yangian parametrized by regular elements of the maximal torus. We study the case of gl(n), where it is known that for a fixed tame representation, and real parameters, the Bethe subalgebras act with simple spectrum. Moreover, they compactify to a family parametrized by the real points of the Deligne-Mumford moduli space of stable genus 0 curves with n+2 marked points. The spectra of this family combine into the fibers of a covering for the moduli space. I will discuss a gl(n) crystal structure on the fibers, which can be described via skew semistandard Young tableaux, and the monodromy action for the covering given by a type of cactus group.

*We will go to a seminar lunch beforehand. If you want to join, please meet Asilata on the ground floor of Hanna Newman Building at noon.