Modular realizations of hyperbolic Weyl groups
Number Theory
2011-05-13 v2 High Energy Physics - Theory
Rings and Algebras
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.
Cite
@article{arxiv.1010.2212,
title = {Modular realizations of hyperbolic Weyl groups},
author = {Axel Kleinschmidt and Hermann Nicolai and Jakob Palmkvist},
journal= {arXiv preprint arXiv:1010.2212},
year = {2011}
}
Comments
35+1 pages, 1 figure. v2: Extended results. In particular, the octonionic realization of W(E10) is completed. Sections and appendices rearranged. References added