2017/10/21 by Gehao Wang, Wang, Gehao
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1710.07764
The Brezin-Gross-Witten (BGW) model is one of the basic examples in the class of non-eigenvalue unitary matrix models. The generalized BGW tau-function τN was constructed from a one parametric deformation of the original BGW model using the generalized Kontsevich model representation. It is a tau-function of the KdV hierarchy for any value of N∈\mathbb C, where the case N=0 reduces to the original BGW tau-function. In this paper, we present a representation of τN in terms of the W1+∞ operators that preserves the KP integrability. This naturally establishes a connection between the (generalized) BGW and Kontsevich-Witten tau-functions using GL(∞) operators, both considered as the basic building blocks in the theory of matrix models and partition functions.