https://doi.org/10.1140/epjc/s10052-024-13067-z
Regular Article - Theoretical Physics
Two 
-ensemble realization of -deformed WLZZ models
1
MIPT, 141701, Dolgoprudny, Russia
2
Lebedev Physics Institute, 119991, Moscow, Russia
3
NRC “Kurchatov Institute”, 123182, Moscow, Russia
4
Institute for Information Transmission Problems, 127994, Moscow, Russia
a mironov@lpi.ru, mironov@itep.ru
Received:
12
June
2024
Accepted:
1
July
2024
Published online:
17
July
2024
We consider a two -ensemble realization of the series of -deformed WLZZ matrix models. We demonstrate that such a realization involves -deformed Harish-Chandra–Itzykson–Zuber integrals, one of them providing a coupling to the external field. We also construct Ward identities in the corresponding two -ensemble model, which requires a set of identities for partition function of the one -ensemble in the external field, and a set of identities for the -deformed Itzykson-Zuber integral. These both sets of identities are formulated in terms of the Dunkl operators.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
