Dunkl-Cherednik operators and quantum Lax pairs
Seminars
Seminar “Modern Mathematical Physics”
Date and Time: Tuesday, 19 December 2017, at 2:30 PM
Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics
Seminar Topic: «Dunkl-Cherednik operators and quantum Lax pairs»
Speaker: Oleg Chalykh (University of Leeds, UK)
Abstract:
We establish a direct link between Dunkl operators and quantum Lax pairs for Calogero-Moser systems. In the elliptic case this produces Lax pairs with spectral parameter that in the classical limit reduce to the well-known Krichever’s Lax pair and its analogues for other root systems, including the BC_n case corresponding to the Inozemtsev system. A similar construction is obtained for the elliptic Ruijsenaars-Schneider system and its variants. The Dunkl operators in that case are replaced by their q-analogues, also known as Cherednik operators. In particular, we find a Lax matrix for the van Diejen-Komori-Hikami system (a BC_n-variant of the elliptic Ruijsenaars system), which remained elusive until now.
The theme participants and everybody interested are kindly invited!