A generating function of the number of homomorphisms from a surface group into a finite group
Quantum Algebra
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate the number of homomorphisms using the decomposition of the group algebra into irreducible factors. This gives a new proof of the classical formulas of Frobenius, Schur, and Mednykh.
Cite
@article{arxiv.math/0209008,
title = {A generating function of the number of homomorphisms from a surface group into a finite group},
author = {Motohico Mulase and Josephine T. Yu},
journal= {arXiv preprint arXiv:math/0209008},
year = {2007}
}
Comments
12 pages, 1 figure. Prepared in AMS-LaTeX