On Higher Brézin–Gross–Witten Tau Functions

In this paper, we consider the higher Brézin–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 W⁽³⁾-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.