Exact Results in Quantum Theory

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.