University of Sydney Algebra Seminar
Iva Halacheva
Friday 4 August, 12-1pm, Place: Carslaw 173
Bethe subalgebras of the Yangian of gl(n), Gelfand-Tsetlin patterns, and cacti
The family of Bethe subalgebras forms a collection of maximal commutative subalgebras of the Yangian indexed by regular elements of the maximal torus. We will focus on the Yangian for gl(n), where it is known that this collection extends to a larger family parametrized by the Deligne-Mumford compactification of M(0,n+2). Taking real points of this parameter space, the corresponding Bethe subalgebras act with simple spectrum on a fixed tame representation, and their spectra assemble into an unramified covering. Moreover, the fiber over any point can be identified with a collection of Gelfand-Tsetlin keystone patterns, and I will discuss how under this isomorphism the monodromy action is given by a type of cactus group. This is joint work with Anfisa Gurenkova and Lenya Rybnikov.