A proof of Harish-Chandra's integrability theorem for cuspidal representations of ${\mathrm{GL}}_n({\mathbb{F}}_{\ell }((t)))$

Avraham Aizenbud, Nir Avni, Dmitry Gourevitch +2

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…