Induced representations and hypergroup homomorphisms

The purpose of this paper is to continue the study of induced representations of hypergroups. We introduce the concept of Weil subhypergroups and Weil homomorphisms and derive a Weil formula for kernels of Weil homomorphisms. Making use of this decomposition formula, we prove in the main theorem that lifting a representation via a Weil homomorphism is compatible with the inducing process. As a further consequence we obtain that a character of a supernormal subhypergroup is inducible, if and only if it admits an extension, while in general the extensibility of a character does not imply its inducibility.This research project is supported by the DFG.