A generating function of the number of homomorphisms from a surface group into a finite group

Details A generating function of the number of homomorphisms from a surface group into a finite group A generating function of the number of homomorphisms from a surface group into a finite group

2002-09-02

arxiv.org/abs/math/0209008v2

Mathematics

Quantum Algebra

12 pages, 1 figure. Prepared in AMS-LaTeX

Scientific paper

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.

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