English

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}
}

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10 pages