1301.5580 (Motohico Mulase et al.)

The spectral curve and the Schroedinger equation of double Hurwitz
numbers and higher spin structures    [PDF]

Motohico Mulase, Sergey Shadrin, Loek Spitz

We derive the spectral curves for $q$-part double Hurwitz numbers, $r$-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0,1)-geometry. We quantize this family of spectral curves and obtain the Schroedinger equations for the partition function of the corresponding Hurwitz problems. We thus confirm the conjecture for the existence of quantum curves in these generalized Hurwitz number cases.

View original: http://arxiv.org/abs/1301.5580