Generalized Brézin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy

Abstract

In this paper, we prove that the generalized Brézin-Gross-Witten tau-function is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim that it describes a spin version of the strictly monotone Hurwitz numbers. A family of the hypergeometric tau-functions of the BKP hierarchy, corresponding to the rational weight generating functions, is investigated. In particular, the cut-and-join operators are constructed, and the explicit description of the BKP Sato Grassmannian points is derived. Representatives of this family can be associated with interesting families of spin Hurwitz numbers including a spin version of the monotone Hurwitz numbers.

27 pages, minor revision

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Cited by in corpus (6)

• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
• Genus expansion of matrix models and $\hslash$ expansion of $B$KP hierarchy
• Action of $W$-type operators on Schur functions and Schur Q-functions
• Action of Virasoro operators on Hall-Littlewood polynomials
• The ordered exponential representation of GKM using the $W_{1+\infty }$ operator