String Theory Journal Club

The Gaussian Hermitian matrix model has the peculiar property that the averages of Schur functions of the eigenvalues take purely factorized forms, and can be written solely in terms of Schur functions evaluated at certain special values. This property, commonly referred to as superintegrability, has also been conjectured in the case of beta-deformed and q/t-deformed matrix models, which involve the Jack and Macdonald polynomials respectively. In this seminar, I will review these notions, and outline a proof of superintegrability in the case of beta-deformed matrix models. This is based on a joint work with A. Bawane and P. Sulkowski.