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Partial Characters and Signed Quotient Hypergroups
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- Journal:
- Canadian Journal of Mathematics / Volume 51 / Issue 1 / 01 February 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 96-116
- Print publication:
- 01 February 1999
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- Article
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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.
