
Journal of Lie Theory 16 (2006), No. 2, 251270 Copyright Heldermann Verlag 2006 Symmetry of Arthur Parameters under Aubert Involution Dubravka Ban Universität Münster, Mathematisches Institut, Einsteinstr. 62, 48149 Münster, Germany Permanent Address: Dept. of Mathematics, Southern Illinois University, Carbondale, IL 62901, U.S.A. dban@math.siu.edu [Abstractpdf] For a generic irreducible representation $\pi$ of the odd orthogonal group SO$(2n+1,F)$ over a $p$adic field $F$, we compute the Aubert involution $\hat{\pi}$ and the corresponding $L$parameter. We show that, among generic representations, only tempered representations are base points attached to $A$parameters and prove that in this case the $A$parameters of $\pi$ and $\hat{\pi}$ are symmetric. In addition, we consider $A$parameters $\psi$ of SO$(2n+1, F)$ corresponding to certain nontempered representations and prove that $\psi$ and $\hat{\psi}$ are symmetric. Keywords: Arthur parameters, Aubert involution, odd orthogonal groups over $p$adic fields. MSC: 22E50, 11F70 [ Fulltextpdf (236 KB)] for subscribers only. 