A note on local periods for supercuspidal representations

Abstract

Let $G$ be a $p$-adic reductive group and $H$ a unimodular spherical subgroup of $G$. Let $\pi$ be a unitary supercuspidal representation of $G$. In this note, under a mild assumption, we show that local periods in $Ho{m}_H(\pi ,\mathbb{C})$ can be constructed by integrating the matrix coefficients of $\pi$ over $H$.

This paper has been withdrawn by the author and the result has been merged into arXiv:1509.06166

References in corpus (3)

• Periods and nonvanishing of central L-values for GL(2n)
• Une variante d'un résultat de Aizenbud, Gourevitch, Rallis et Schiffmann
• An orthogonality relation for spherical characters of supercuspidal representations