On pentagon identity in Ding-Iohara-Miki algebra

被引：0
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作者：
Yegor Zenkevich
机构：
[1] Scuola Internazionale Superiore di Studi Avanzati (SISSA),Institute for Theoretical and Mathematical Physics (ITMP)
[2] INFN,undefined
[3] Sezione di Trieste,undefined
[4] Institute for Geometry and Physics (IGAP),undefined
[5] Institute for Theoretical and Experimental Physics (ITEP),undefined
[6] Lomonosov Moscow State University,undefined
来源：
Journal of High Energy Physics | / 2023卷
关键词：
Quantum Groups; Conformal and W Symmetry;
D O I：
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学科分类号：
摘要：
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.
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