  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.
