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Pré-Publication, Document De Travail Année : 2016

Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation

Résumé

Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck's dessin d'enfant D and that most standard graphs and finite geometries G-such as near polygons and their generalizations-are stabilized by a D. In our paper, tripods P − D − G of rank larger than two, corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G ′ s have a contextuality parameter close to its maximal value 1.
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Dates et versions

hal-01256894 , version 1 (15-01-2016)

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Michel Planat, Hishamuddin Zainuddin. Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation. 2016. ⟨hal-01256894⟩
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