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Partial Characters and Signed Quotient Hypergroups
Published online by Cambridge University Press: 20 November 2018
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 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.
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- Research Article
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- Copyright © Canadian Mathematical Society 1999
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