Weighted Hurwitz numbers, $\tau$-functions and matrix integrals
Abstract
The basis elements spanning the Sato Grassmannian element corresponding to the KP -function that serves as generating function for rationally weighted Hurwitz numbers are shown to be Meijer -functions. Using their Mellin-Barnes integral representation the -function, evaluated at the trace invariants of an externally coupled matrix, is expressed as a matrix integral. Using the Mellin-Barnes integral transform of an infinite product of functions, a similar matrix integral representation is given for the KP -function that serves as generating function for quantum weighted Hurwitz numbers.
Keywords
Cite
@article{arxiv.2002.07935,
title = {Weighted Hurwitz numbers, $\tau$-functions and matrix integrals},
author = {J. Harnad},
journal= {arXiv preprint arXiv:2002.07935},
year = {2021}
}
Comments
11 pages. Text of invited presentation at: Quantum Theory and Symmetries, XIth International symposium, Centre de recherches math\'ematiques, Montr\'eal, July 1-5, 2019