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

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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.
12 pages, 1 figure. Prepared in AMS-LaTeX

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Quantum Algebra, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/64821

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209008
 http://arxiv.org/abs/math/0209008

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arXiv