Stabilite en niveau 0 pour les groupes orthogonaux impairs p-adiques
Stabilite en niveau 0 pour les groupes orthogonaux impairs p-adiques
摘要：
本文构造了p-进域上奇正交群椭圆元集合上的稳定分布。这些分布均为零水平分布。它们被Langlands参数化。在本文的第二部分，我们展示了如何根据离散序列的特征来解释这些分布，这是以A. M. Aubert提出了如何利用Lusztig归纳法将零能级的情形还原为幂幺约化的情形。但是，模这个明确的假设，我们证明了我们的计算将确定所有稳定的线性组合的离散系列的零水平$SO(2n+1)$。利用参数集上的类傅立叶对合，将离散级数的稳定分布和稳定线性组合的参数联系起来。
英文摘要：
In this paper, we construct stable distributions on the set of elliptic elements of an odd orthogonal groups (over a p-adic field with p large). Theses distributions are of zero level. They are parametrised by Langlands like parameters. In the second part of the paper, we show how to interpret these distributions in term of characters of discrete series; this is conditional to a result of A.-M. Aubert which announces how to reduce the zero level case to the case of unipotent reduction using the Lusztig's induction. But, modulo this explicit hypothesis, we prove that our computation will determine all the stable linear combinations of discrete series of zero level for $SO(2n+1)$. The link between the parameters of stable distributions and stable linear combinations of discrete series is done by using a Fourier like involution on the set of parameters.
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