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 a surface group into a finite group

  • Author(s): Mulase, Motohico
  • Yu, Josephine T.
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0209008.pdf
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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.

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