2025/09/24 by A. Yu. Orlov, Orlov, A. Yu.
Mathematics · #Spectral Theory in Mathematical Physics #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2509.20213
We present a family of solvable multi-matrix models associated with an arbitrary embedded graph Γ with a single vertex. The graph with n edges is equipped with 2n corner matrices. The partition function of each member of the family depends on the set of eigenvalues of monodromies of corner matrices around the vertices of the dual graph Γ^* and sets of parameters attached to each vertex of Γ. We select the cases where the partition function of a model is a tau function of KP, 2KP and BKP hiearachies. We compare integrals over U(N) and over SU(N) groups. In U(N) case there is no restriction on the number of vertices of Γ. We also consider mixed ensembles of matrices from GL(N),U(N) and SU(N).