论文标题
une mesure de Radon Invariante Sur Les $ f $ strates Unipotentes
Une mesure de Radon invariante sur les $F$-strates unipotentes
论文作者
论文摘要
令$ f $为非一切本紧凑的领域，$ g $ a连接的还原组定义了$ f $。对于$ g（f）$中的任何一项单位元素$ u $，我们都在[l] a $ f $ -stratum $ \ boldsymbol {\ mathfrak {\ mathfrak {y}} _ {f，u} $中，这是（可能是无限）的$ g（f）$ - 或者。我们在这里定义一个“规范”非零正$ g（f）$ - $ \ boldsymbol {\ mathfrak {y}} _ {f，u} $上不变ra。在其他假设下，我们推断出与$ u $的$ g（f）$轨道相关的轨道积分的融合。该结构在任何特征上有效，概括了Deligne-ranga rao [rr]，也适用于$ \ textrm {lie}（g）（f）$中的nilpotent Strata。
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 $\boldsymbol{\mathfrak{Y}}_{F,u}$ 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 $\boldsymbol{\mathfrak{Y}}_{F,u}$. 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 $\textrm{Lie}(G)(F)$.
