Abstract:Consider the Chevalley map $$ p:\mathfrak{gl} _n(F)\to (\mathfrak{gl}_n//\mathrm{GL}_n)(F), $$ where $F=\mathbb{F}_\ell((t))$. We show that the push forward via $p$ of every smooth compactly supported measure on $\mathfrak{gl}_n(F)$ is a measure whose density belongs to $L^q$ for every finite $q$.
As a consequence, using the main result of [AGKSc], we obtain local integrability for Harish--Chandra's characters of irreducible cuspidal representations of $\mathrm{GL}_n(F)$.
From: Avraham Aizenbud [view email]
[v1]
Fri, 12 Jun 2026 09:01:10 UTC (52 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。