Une mesure de Radon invariante sur les $F$-strates unipotentes

Abstract

Let $F$ be a non-Archimedean locally compact field and $G$ a connected reductive group defined over $F$. To any unipotent element $u$ in $G(F)$, we have associated in [L] an $F$-stratum ${\mathfrak{Y}}_{F,u}$ which is a (possibly infinite) union of unipotent $G(F)$-orbits. We define here a "canonical" non-zero positive $G(F)$-invariant Radon measure on ${\mathfrak{Y}}_{F,u}$. Under additional assumptions, we deduce the convergence of the orbital integral associated to the $G(F)$-orbit of $u$. The construction, valid in any characteristic, generalizes the one of Deligne-Ranga Rao [RR] and also applies to nilpotent strata in $\text{Lie}(G)(F)$.

in French language, 43 pages

References in corpus (1)

• Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I

Cited by in corpus (1)

• Développement fin de la contribution unipotente à la formule des traces sur un corps global de caractéristique p>0, I