Modular realizations of hyperbolic Weyl groups

Axel Kleinschmidt; Hermann Nicolai; Jakob Palmkvist

Modular realizations of hyperbolic Weyl groups

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arxiv 1010.2212 v2 pith:WZY6KUXM submitted 2010-10-11 math.NT hep-thmath.RA

Axel Kleinschmidt , Hermann Nicolai , Jakob Palmkvist This is my paper

classification math.NThep-thmath.RA

keywords groupsmodularweyldomainsgrouphyperbolicintegeralgebras

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We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group.

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