Q-Polynomial expansion for Brezin-Gross-Witten tau-function

TL;DR

This paper proves that the Brezin-Gross-Witten tau-function is a hypergeometric tau function of the BKP hierarchy, enabling a new representation as a linear combination of Schur Q-polynomials with geometric significance.

Contribution

It confirms a conjecture that BGW tau-functions are hypergeometric BKP tau functions and provides a new Schur Q-polynomial expansion with simple coefficients.

Findings

BGW tau-function is hypergeometric BKP tau function

Original BGW tau-function can be expressed as a Schur Q-polynomial linear combination

Supports geometric interpretations of BGW tau-function

Abstract

In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In particular, this shows that the original BGW tau-function, which has enumerative geometric interpretations, can be represented as a linear combination of Schur Q-polynomials with simple coefficients.