https://doi.org/10.1140/epjc/s10052-022-10466-y
Regular Article - Theoretical Physics
Superintegrability in 
-deformed Gaussian Hermitian matrix model from W-operators
1
MIPT, 141701, Dolgoprudny, Russia
2
Lebedev Physics Institute, 119991, Moscow, Russia
3
ITMP MSU, 119991, Moscow, Russia
4
NRC “Kurchatov Institute”, 117218, Moscow, Russia
Received:
6
April
2022
Accepted:
23
May
2022
Published online:
22
June
2022
This paper is devoted to the phenomenon of superintegrability. This phenomenon is manifested in the existence of a formula for character averages, expressed through the same characters at special points and of its various generalization. In this paper we develop a method of proving such formulas from first principle from Virasoro constraints and W-representation. We apply it to prove the formula for the Jack functions averages – appropriate analogue of characters for the -deformed Hermitian Gaussian matrix model. We also sketch the construction of W-operators from Calogero–Ruijsenaars Hamiltonians.
© The Author(s) 2022
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