Abstract

Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide τ-functions for several hierarchies of integrable equations. In this paper, we construct the matrix integral solutions to the Leznov lattice equation, semi-discrete and fully-discrete version and the Pfaffianized Leznov lattice systems, respectively. We demonstrate that the partition function of the Jacobi type unitary ensemble is a solution to the semi-discrete Leznov lattice and the partition function of the Jacobi type orthogonal/symplectic ensemble solves the Pfaffianized Leznov lattice.

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