4 papers
Rank recursion for -Whittaker and Macdonald operators
Philippe Di Francesco, Hieu Trung Vu
In this paper, we introduce and prove a set of rank recurrence relations for -Whittaker and Macdonald operators. We also derive an explicit expression for the -th power of th…
Arctic curves of the T-system with Slanted Initial Data
Philippe Di Francesco, Hieu Trung Vu
We study the T-system of type , also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. D…
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…