BIMSA > Integrable systems blackboard seminar Integrable systems blackboard seminar R-matrix Dunkl operators and spin Calogero–Moser models for classical root systems
R-matrix Dunkl operators and spin Calogero–Moser models for classical root systems
Organizers
Andrii Liashyk , Nicolai Reshetikhin , Ruijie Xu
Speaker
Maria Matushko
Time
Monday, November 9, 2026 3:30 PM - 4:30 PM
Venue
A7-201
Abstract
We introduce R-matrix Dunkl operators for an arbitrary root system, with commutativity controlled by the corresponding associative Yang–Baxter equations. In the elliptic setting our main examples are of types A_n and BC_n: for type A_n one recovers the Baxter–Belavin R-matrix picture, while for type BC_n the same framework involves the Baxter–Belavin R-matrix together with a suitable boundary K-matrix. In both cases we construct commuting quantum Hamiltonians giving an R-matrix quantisation of the corresponding classical system, obtain an R-matrix valued quantum Lax pair, and produce commuting conserved charges for the associated long-range quantum spin chain. The talk is based on the joint work with Oleg Chalykh.