Homogeneous distributions on finite dimensional vector spaces

Abstract

Let $V$ be a finite dimensional vector space over a local field $F$. Let $\chi :F^{\times }\to {\mathbb{C}}^{\times }$ be an arbitrary character of $F^{\times }$. We determine the structure of the natural representation of $\mathrm{GL}(V)$ on the space ${\mathcal{S}}^{\ast }(V{)}^{\chi }$ of $\chi$-invariant distributions on $V$.

References in corpus (2)

• Schwartz functions on Nash manifolds
• A proof of the Howe duality conjecture

Cited by in corpus (1)

• On the nonvanishing hypothesis for Rankin-Selberg convolutions for ${\mathrm{GL}}_n(\mathbb{C})\times {\mathrm{GL}}_n(\mathbb{C})$