On pentagon identity in Ding-Iohara-Miki algebra
Quantum Algebra
2021-12-30 v1 High Energy Physics - Theory
Abstract
We notice that the famous pentagon identity for quantum dilogarithm functions and the five-term relation for certain operators related to Macdonald polynomials discovered by Garsia and Mellit can both be understood as specific cases of a general "master pentagon identity" for group-like elements in the Ding-Iohara-Miki (or quantum toroidal, or elliptic Hall) algebra. We perform some checks of this remarkable identity and discuss its implications.
Keywords
Cite
@article{arxiv.2112.14687,
title = {On pentagon identity in Ding-Iohara-Miki algebra},
author = {Yegor Zenkevich},
journal= {arXiv preprint arXiv:2112.14687},
year = {2021}
}
Comments
10 pages