2024/12/23 by Chidambaram, Nitin Kumar, Dołęga, Maciej, Osuga, Kento
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2412.17502
We prove that single G-weighted \mathfrakb-Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights G. Consequently, the \mathfrakb-Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of \mathfrakb-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.