@article{c3803195dbb54791aa675b49483dc4b6,
title = "Ruijsenaars wavefunctions as modular group matrix coefficients",
abstract = "We give a description of the Halln{\"a}s–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element S∈SL(2,Z) acting on the Hilbert space of GL(2) quantum Teichm{\"u}ller theory on the punctured torus. The GL(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed GL(2)-local systems on the punctured torus, and an SL(2,Z)-equivariant embedding of the GL(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.",
keywords = "13F60, 17B37, 81R12, Cluster varieties, Ruijsenaars wavefunctions, Spherical DAHA",
author = "{Di Francesco}, Philippe and Rinat Kedem and Sergey Khoroshkin and Gus Schrader and Alexander Shapiro",
note = "We are grateful to Mingyuan Hu, Nicolai Reshetikhin, J\u00F6rg Teschner, and Eric Zaslow for helpful discussions and to anonymous referees for many useful suggestions and corrections. P.D.F. is supported by the Morris and Gertrude Fine Endowment and the Simons Foundation Grant MP-TSM-00002262. R.K. acknowledges support from the Simons Foundation Grant MP-TSM-00001941. S.Kh. is grateful to the University of Edinburgh for its hospitality during the fall semester of 2023. The work of S.Kh. is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University). G.S. has been supported by the NSF Standard Grant DMS-2302624. A.S. has been supported by the European Research Council under the European Union\u2019s Horizon 2020 research and innovation program under Grant Agreement No 948885 and by the Royal Society University Research Fellowship.",
year = "2024",
month = dec,
doi = "10.1007/s11005-024-01881-1",
language = "English (US)",
volume = "114",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Netherlands",
number = "6",
}