BIMSA > BIMSA Integrable Systems Seminar Limit shapes of probability measures in representation theory of U_q(sl_2) at roots of unity
Limit shapes of probability measures in representation theory of U_q(sl_2) at roots of unity
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Dmitry Solovyev
Time
Tuesday, December 16, 2025 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711 (BIMSA)
Abstract
Limit shape phenomenon emerges in systems with random behavior. It manifests a formation of the most probable state, where all other macroscopically different states are exponentially improbable. In this talk, we explore such phenomena in the Grothendieck ring of the category of tilting modules for the quantum group U_q(sl_2) with divided powers, where q is an even root of unity. Considering large tensor powers of the defining representation, we describe the most probable trajectory in the main Weyl chamber with respect to the character probability measure and analyze fluctuations around this limit shape. This talk is based on arXiv:2404.03933, a joint work with A. Lachowska, O. Postnova and N. Reshetikhin.