Q-Polynomial expansion for Brezin-Gross-Witten 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.