Vanishing at infinity on homogeneous spaces of reductive type. (15th April 2016)

• Record Type: Journal Article
• Authors: Krötz, Bernhard; Sayag, Eitan; Schlichtkrull, Henrik
• Is Part Of: Compositio mathematica. Volume 152:Number 7(2016:Jul.)
• Page Start: 1385
• Page End: 1397
• Publication Date: 2016-04-15
• Subjects: 22F30, -- 22E46, -- 53C35 (primary); homogeneous space, -- representation, -- smooth vector; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007399
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : Let $G$ be a real reductive group and $Z=G/H$ a unimodular homogeneous $G$ space. The space $Z$ is said to satisfy VAI (vanishing at infinity) if all smooth vectors in the Banach representations $L^{p}(Z)$ vanish at infinity, $1\leqslant p<\infty$ . For $H$ connected we show that $Z$ satisfies VAI if and only if it is of reductive type.