- 可积系统黑板讨论班

R-matrix Dunkl operators and spin Calogero–Moser models for classical root systems

组织者

安德烈·利亚希克 , 尼古拉·莱舍提金 , 许睿捷

演讲者

Maria Matushko

时间

2026年11月09日 15:30 至 16:30

地点

A7-201

摘要

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.