TL;DR
This paper introduces a generating function for spin Hurwitz numbers that is a tau function of the 2-BKP hierarchy and relates it as a square root to a tau function of the 2-KP hierarchy, revealing deep integrable structure.
Contribution
It demonstrates that the generating function for spin Hurwitz numbers is a tau function of the 2-BKP hierarchy and connects it as a square root to a 2-KP tau function, advancing understanding of their integrable properties.
Findings
The generating function for spin Hurwitz numbers is a 2-BKP tau function.
It is a square root of a 2-KP tau function.
Establishes a new link between spin Hurwitz numbers and integrable hierarchies.
Abstract
We exhibit a generating function of spin Hurwitz numbers analogous to (disconnected) double Hurwitz numbers that is a tau function of the two-component BKP (2-BKP) hierarchy and is a square root of a tau function of the two-component KP (2-KP) hierarchy defined by related Hurwitz numbers.
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