Modular realizations of hyperbolic Weyl groups

2010/10/11 by Axel Kleinschmidt, Hermann Nicolai, Kleinschmidt, Axel +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1010.2212

Abstract

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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