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Proving superintegrability in $\beta$-deformed eigenvalue models

Aditya Bawane, Pedram Karimi, Piotr Sułkowski

SciPost Phys. 13, 069 (2022) · published 27 September 2022


In this note we provide proofs of various expressions for expectation values of symmetric polynomials in $\beta$-deformed eigenvalue models with quadratic, linear, and logarithmic potentials. The relations we derive are also referred to as superintegrability. Our work completes proofs of superintegrability statements conjectured earlier in literature.

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