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Journal of Lie Theory 24 (2014), No. 1, 159--178
Copyright Heldermann Verlag 2014

An Imprimitivity Theorem for Representations of a Semi-Direct Product Hypergroup

Herbert Heyer
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Satoshi Kawakami
Dept. of Mathematics, Nara University of Education, Takabatake-cho, Nara 630-8528, Japan


The purpose of the present paper is to establish an imprimitivity theorem for representations of a semi-direct product hypergroup $K = H \rtimes_\beta G$ defined by a smooth action $\beta$ of a locally compact group $G$ on a hypergroup $H$. The proof of the theorem relies on a smooth irreducible absorbing action $\alpha$ of $K$ on a locally compact space $X$ and on an imprimitivity condition for the triplet $(K, C_0(X), \alpha)$.

Keywords: Induced representation, imprimitivity theorem, hypergroup.

MSC: 22D30, 22F50, 20N20, 43A62

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