130 citations · 1.2k across the 44 of their papers we have counts for
49 papers
Cluster structure on genus 2 spherical DAHA: seven-colored flower
Semeon Arthamonov, Leonid Chekhov, Philippe Di Francesco +4
We construct an embedding of the Arthamonov-Shakirov algebra of genus 2 knot operators into the quantized coordinate ring of the cluster Poisson variety of exceptional finite mutat…
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 Duality and the proof of the Quantum Q-system conjecture
Philippe Di Francesco, Rinat Kedem
The -symmetry of Cherednik's spherical double affine Hecke algebras in Macdonald theory includes a distinguished generator which acts as a discrete time evolution…
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…