Partial characters and signed quotient hypergroups

Abstract

If G is a closed subgroup of a commutative hypergroup K, then the coset space K/G carries a quotient hypergroup structure. In this paper, we study related convolution structures on K/G coming from deformations of the quotient hypergroup structure by certain functions on K which we call partial characters with respect to G. They are usually not probability-preserving, but lead to so-called signed hypergroups on K/G. A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair (U(n, 1), U(n)) are discussed.