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arXiv · 2203.15675

Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators

V. Mishnyakov·A. Oreshina
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Abstract

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 $\beta$-deformed Hermitian Gaussian matrix model. We also sketch the construction of $W$-operators from Calogero-Ruijsenaars Hamiltonians.

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V. Mishnyakov, A. Oreshina. 2022-03-29. Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators. https://doi.org/10.1140/epjc%2Fs10052-022-10466-y

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