The theory of $q$-Whittaker functions for classical types is known to have a (quantum) cluster algebra realization. In this framework, a natural connection with the quantum dilogarithm is known. We show how this extends to the more general case of Macdonald theory in type A. We propose new Givental-like and Mellin-Barnes-like expressions for the Macdonald functions, and explore their properties. These involve heavy use of quantum dilogarithms. (ongoing collaboration with M. Bershtein, J.-E. Bourgine, R. Kedem, V. Pasquier and J. Shiraishi).
By Gleb Koshevoy
By Lucas Pannier
By Anastasia Matveeva
By Arthemy Kiselev
By Thomas Simon
By Vladimir Dotsenko
By Toshiki Nakashima
By Oleg Kaikov
By Reiko Toriumi
By Thomas Müller
By Cyril Banderier
By Marek Bożejko
By Hiroaki Nakamura
By Kilian Raschel
By Pierre-Vincent Koseleff
By Parham Radpay
By Paul Kiefer
By Salim Tayou
