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January 2012 Modular realizations of hyperbolic Weyl groups
Axel Kleinschmidt, Hermann Nicolai, Jakob Palmkvist
Adv. Theor. Math. Phys. 16(1): 97-148 (January 2012).

Abstract

We study the recently discovered isomorphisms between hyperbolic Weyl groups and modular groups over integer domains in normed division algebras. We show how to realize the group action via fractional linear transformations on generalized upper half-planes over the division algebras, focusing on the cases involving quaternions and octonions. For these we construct automorphic forms, whose explicit expressions depend crucially on the underlying arithmetic properties of the integer domains. Another main new result is the explicit octavian realization of $W+(E_{10})$, which contains as a special case a new realization of $W+(E_8)$ in terms of unit octavians and their automorphism group.

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Axel Kleinschmidt. Hermann Nicolai. Jakob Palmkvist. "Modular realizations of hyperbolic Weyl groups." Adv. Theor. Math. Phys. 16 (1) 97 - 148, January 2012.

Information

Published: January 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1280.81064
MathSciNet: MR3019404

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 1 • January 2012
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