English

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.

Keywords

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