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Ruijsenaars wavefunctions as modular group matrix coefficients
Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin +2
We give a description of the Hallnäs--Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element $S\in SL(2,\mathbb{Z…
Duality and Macdonald difference operators
Philippe Di Francesco, Rinat Kedem
This note summarizes certain properties common to Macdonald, Koornwinder and Arthamonov-Shakirov -difference operators, relating to the duality or bi-spectrality properties of t…
Macdonald operators and quantum Q-systems for classical types
Philippe Di Francesco, Rinat Kedem
We propose solutions of the quantum Q-systems of types in terms of -difference operators, generalizing our previous construction for the Q-system of type . The…
(t,q) Q-systems, DAHA and quantum toroidal algebras via generalized Macdonald operators
Philippe Di Francesco, Rinat Kedem
We introduce difference operators on the space of symmetric functions which are a natural generalization of the -Macdonald operators. In the limit, they satisfy…
T-systems and the pentagram map
Rinat Kedem, Panupong Vichitkunakorn
These notes summarize two different connections between two discrete integrable systems, the -system and its infinite-rank analog, the octahedron relation, and the pentagr…
Fermionic spectra in integrable systems
Rinat Kedem
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantu…