Exact Results in Quantum Theory & Gravity

Multipoint correlation functions can be expanded as an average of different bases (characters) in the space of symmetric polynomials. It turns out that for many models there exists a basis where the average of character takes a simple factorized form , written in the term of character again. This character preservation property is called superintegrability. In this talk, I will review and outline the proof of superintegrability in the beta deformed eigenvalue models. This is based on a joint work with A. Bawane and P. Sułkowski.