Using the theory of classical domains and Jack polynomials, we generalize several integrals over the unitary group, due to Fyodorov and Khoruzhenko, to integrals over the circular orthogonal and circular symplectic ensembles. While in the unitary case a fundamental role is played by complex matrices, it is anti-symmetric and symmetric matrices which play the same role in the latter two cases. In our workings, a generalization of the evaluation of the integral of a Jack polynomial times the Selberg weight sought by Fyodorov and Khoruzhenko is identified.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.