
Journal of Lie Theory 24 (2014), No. 1, 159178 Copyright Heldermann Verlag 2014 An Imprimitivity Theorem for Representations of a SemiDirect Product Hypergroup Herbert Heyer Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany herbert.heyer@unituebingen.de Satoshi Kawakami Dept. of Mathematics, Nara University of Education, Takabatakecho, Nara 6308528, Japan kawakami@naraedu.ac.jp [Abstractpdf] The purpose of the present paper is to establish an imprimitivity theorem for representations of a semidirect 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 [ Fulltextpdf (328 KB)] for subscribers only. 