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Seminar
FIELD Phys:StringTheory
DATE May 23 (Mon), 2022
TIME 17:00-18:00
PLACE Online
SPEAKER Chalykh, Oleg
HOST Ghim, Dongwook
INSTITUTE Leeds University
TITLE Twisted Ruijsenaars models
ABSTRACT The quantum Ruijsenaars model is a q-analogue of the Calogero?Moser model, described by n commuting partial difference operators (quantum hamiltonians) h_1, …, h_n. Its trigonometric variant is closely related to Macdonald polynomials and DAHAs. It turns out that for each natural number \ell>1, there exists an integrable system whose quantum hamiltonians look, loosely speaking, as the \ell-th powers of h_1, …, h_n. I will discuss several ways of arriving at this generalisation. In the elliptic case, the deformation parameter (“twisting”) is an arbitrary \ell-torsion point c on the underlying elliptic curve; when c=0 one gets precisely the \ell-th powers of h_1, …, h_n. The construction works for all root systems, including the Van Diejen's system (BC_n case) - the existence of such a twisted version of the Van Diejen's system was previously conjectured by Eric Rains.
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