On Higher BrAzin-Gross-Witten Tau Functions

Abstract

In this paper, we consider the higher BrAzin-Gross-Witten (BGW) tau functions, given by the matrix integrals. For these tau functions we construct the canonical Kac-Schwarz operators, quantum spectral curves, and -constraints. For the simplest representative we construct the cut-and-join operators, which describe the algebraic version of the topological recursion. We also investigate a one-parametric generalization of the higher BGW tau functions.