On pentagon identity in Ding-Iohara-Miki algebra
- Resource Type
- article
- Authors
- Yegor Zenkevich
- Source
- Journal of High Energy Physics, Vol 2023, Iss 3, Pp 1-14 (2023)
- Subject
- Quantum Groups
Conformal and W Symmetry
Nuclear and particle physics. Atomic energy. Radioactivity
QC770-798
- Language
- English
- ISSN
- 1029-8479
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 prove this curious identity and discuss its implications.