Partial Characters and Signed Quotient Hypergroups

Rösler, Margit ; Voit, Michael

Canadian journal of mathematics, Tome 51 (1999) no. 1, pp. 96-116

Résumé

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 fromdeformations 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 $[0,\infty [$ , which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair $\left( U\left( n,1 \right),\,U\left( n \right) \right)$ are discussed.

Détail

DOI : 10.4153/CJM-1999-006-6

Mots-clés : 43A62, 33C25, 43A20, 43A90, quotient hypergroups, signed hypergroups, Laguerre convolution, Jacobi functions

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