Modular realizations of hyperbolic Weyl groups

Kleinschmidt, Axel; Nicolai, Hermann; Palmkvist, Jakob

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Modular realizations of hyperbolic Weyl groups

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Kleinschmidt, Axel
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Palmkvist, Jakob
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1010.2212v1.pdf
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AdvTheoMath Phys16_97.pdf
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Kleinschmidt, A., Nicolai, H., & Palmkvist, J. (2012). Modular realizations of hyperbolic Weyl groups. Advances in Theoretical and Mathematical Physics, 16(1), 97-148.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-BD4B-3

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.