Proving superintegrability in $\beta$-deformed eigenvalue models

Abstract

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.

arXiv comment13 pages

References in corpus (12)

• Introduction to Random Matrices - Theory and Practice
• Torus knots and mirror symmetry
• Difference equations and symmetric polynomials defined by their zeros
• On the complete perturbative solution of one-matrix models
• Matrix models for $\beta$-ensembles from Nekrasov partition functions
• Ward identities and combinatorics of rainbow tensor models
• On (q,t)-deformation of Gaussian matrix model
• On matrix models and their $q$-deformations
• New Insights into Superintegrability from Unitary Matrix Models
• Superintegrability in $\beta$-deformed Gaussian Hermitian matrix model from $W$-operators
• Applications of Laplace-Beltrami operator for Jack polynomials
• A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials