Journal of Lie Theory 28 (2018), No. 1, 033--041
Copyright 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
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