Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 28 (2018), No. 1, 033--041Copyright Heldermann Verlag 2018 Homogeneous Distributions on Finite Dimensional Vector Spaces Huajian Xue Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China xuehuajian@126.com [Abstract-pdf] Let $V$ be a finite dimensional vector space over a local field $F$. Let $\chi\colon F^\times \rightarrow \C^\times$ be an arbitrary character of $F^\times$. We determine the structure of the natural representation of GL$(V)$ on the space ${\cal S}^*(V)^\chi$ of $\chi$-invariant distributions on $V$. Keywords: Representation, Schwartz function, tempered distribution, degenerate principal series. MSC: 22E50 [ Fulltext-pdf  (254  KB)] for subscribers only.