Connected $(n,m)$-Point Functions of Diagonal $2$-BKP Tau-Functions, and Spin Double Hurwitz Numbers

TL;DR

This paper derives explicit formulas for connected $(n,m)$-point functions of diagonal $2$-BKP tau-functions using fermionic methods and applies these to compute connected spin double Hurwitz numbers, extending previous work to type $B$.

Contribution

It provides a new explicit formula for connected $(n,m)$-point functions of diagonal $2$-BKP tau-functions and applies it to compute spin double Hurwitz numbers in type $B$.

Findings

Explicit formula for connected $(n,m)$-point functions derived.

Application to compute connected spin double Hurwitz numbers.

Extension of previous type $A$ results to type $B$.

Abstract

We derive an explicit formula for the connected $(n,m)$-point functions associated to an arbitrary diagonal tau-function of the $2$-BKP hierarchy using computation of neutral fermions and boson-fermion correspondence of type $B$, and then apply this formula to the computation of connected spin double Hurwitz numbers. This is the type $B$ analogue of \cite{wy2}.