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Partial Characters and Signed Quotient Hypergroups

Published online by Cambridge University Press:  20 November 2018

Margit Rösler  and
Michael Voit
Margit Rösler
Affiliation:
Zentrum Mathematik, Technische Universität München, Arcisstr. 21, D-80290 München, Germany email: roesler@ma.tum.de
Michael Voit
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany email: voit@uni-tuebingen.de
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Abstract

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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.

Keywords

43A6233C2543A2043A90quotient hypergroupssigned hypergroupsLaguerre convolutionJacobi functions
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 1 , 01 February 1999 , pp. 96 - 116
Copyright
Copyright © Canadian Mathematical Society 1999

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