(Springer, 2026-03-14) Chidambaram, Nitin Kumar; Dołęga, Maciej; Osuga, Kento; European Research Council (ERC); Agencia Estatal de Investigación (España)
We prove that single 𝐺-weighted 𝔟-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights 𝐺. Consequently, the 𝔟-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of 𝔟-monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre 𝛽-ensembles are computed by refined topological recursion.
