Classification and Galois conjugacy of Hamming maps

Details Classification and Galois conjugacy of Hamming maps Classification and Galois conjugacy of Hamming maps

2010-06-02

arxiv.org/abs/1006.0516v1

Mathematics

Combinatorics

Scientific paper

We show that for each d>0 the d-dimensional Hamming graph H(d,q) has an orientably regular surface embedding if and only if q is a prime power p^e. If q>2 there are up to isomorphism \phi(q-1)/e such maps, all constructed as Cayley maps for a d-dimensional vector space over the field of order q. We show that for each such pair d, q the corresponding Belyi pairs are conjugate under the action of the absolute Galois group, and we determine their minimal field of definition. We also classify the orientably regular embedding of merged Hamming graphs for q>3.

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