BIMSA > BIMSA Integrable Systems Seminar Bethe subalgebras and Kirillov-Reshetikhin crystals
Bethe subalgebras and Kirillov-Reshetikhin crystals
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Leonid Rybnikov
Time
Friday, March 10, 2023 5:00 PM - 6:30 PM
Venue
A6-101
Abstract
Bethe subalgebras form a family of maximal commutative subalgebras of the Yangian of a simple Lie algebra, parametrized by regular elements of the corresponding adjoint Lie group. We introduce an affine (Kirillov-Reshetikhin) crystal structure on the set of eigenlines for a Bethe subalgebra in a representation of the Yangian (under certain conditions on the representation, satisfied by all tensor products of Kirillov-Reshetikhin modules in type A). This helps to describe the monodromy of solutions of Bethe ansatz for the corresponding XXX Heisenberg magnet chain. This is a joint project with Inna Mashanova-Golikova and Vasily Krylov.