University of Salento Conferences Portal, PMNP 2017: 50 years of IST

Font Size: 
Dunkl--Cherednik operators and quantum Lax pairs
Oleg Chalykh

Last modified: 2017-04-14


We explain that a Dunkl operator can be interpreted as a quantum Lax matrix for the Calogero--Moser system. This interpretation also provides a companion matrix $A$ so that $L, A$ form a quantum Lax pair. The same construction, with Dunkl operators replaced by their q-analogues, known as Cherednik operators, leads to quantum Lax pairs for the relativistic Calogero--Moser system given by the trigonometric Macdonald--Ruijsenaars operators (and Koornwinder--van Diejen operators in the $BC_n$-case). This gives a uniform construction of both classical and quantum Lax pairs for the systems of Ruijsenaars--Schenider type for all root systems, including the Koornwinder--van Diejen system with five coupling parameters.

Full Text: LaTeX