DOCUMENTA MATHEMATICA, Vol. 9 (2004), 527-564

Colette Moeglin

Stabilité en Niveau 0, pour les Groupes Orthogonaux Impairs $p$-Adiques

The general problem we discuss in this paper is how to prove stability properties for a linear combination of characters of irreductible discrete series of p-adic groups. Here we give ideas on how to reduce the case where the Langlands parameter is trivial on the wild ramification group to the case where this Langlands parameter factorizes through the Frobenius; we handle only the case of an odd orthogonal group. The principal result is that the localization commutes with the Lusztig's induction.

2000 Mathematics Subject Classification: 22E50

Keywords and Phrases: representations of p-adic groups, stability, discrete series, Langands parameter

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