Partial Characters and Signed Quotient Hypergroups

<jats:title>Abstract</jats:title><jats:p>If<jats:italic>G</jats:italic>is a closed subgroup of a commutative hypergroup<jats:italic>K</jats:italic>, then the coset space<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>carries a quotient hypergroup structure. In this paper, we study related convolution structures on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>coming fromdeformations of the quotient hypergroup structure by certain functions on<jats:italic>K</jats:italic>which we call partial characters with respect to<jats:italic>G</jats:italic>. They are usually not probability-preserving, but lead to so-called signed hypergroups on<jats:italic>K</jats:italic>/<jats:italic>G</jats:italic>. 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 (<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>, 1),<jats:italic>U</jats:italic>(<jats:italic>n</jats:italic>)) are discussed.</jats:p>