The definability criteria for convex projective polyhedral reflection groups

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Following Vinberg, we find the criteria for a subgroup generated by reflections and its finite-index subgroups to be definable over where is an integrally closed Noetherian ring in the field . We apply these criteria for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the -dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to . Finally we provide some examples of -representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in that are definable over . These were known by Goldman, Benoist, and so on previously.
Publisher
SPRINGER
Issue Date
2015-04
Language
English
Article Type
Article
Keywords

ORBIFOLDS; CONES

Citation

GEOMETRIAE DEDICATA, v.175, no.1, pp.323 - 346

ISSN
0046-5755
DOI
10.1007/s10711-014-9949-3
URI
http://hdl.handle.net/10203/197718
Appears in Collection
MA-Journal Papers(저널논문)
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