Symmetry of Arthur Parameters under Aubert Involution
Journal of Lie Theory, Tome 16 (2006) no. 2, pp. 251-270
Voir la notice de l'article provenant de la source Heldermann Verlag
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.
Classification :
22E50, 11F70
Mots-clés : Arthur parameters, Aubert involution, odd orthogonal groups over $p$-adic fields
Mots-clés : Arthur parameters, Aubert involution, odd orthogonal groups over $p$-adic fields
D. Ban. Symmetry of Arthur Parameters under Aubert Involution. Journal of Lie Theory, Tome 16 (2006) no. 2, pp. 251-270. http://geodesic.mathdoc.fr/item/JOLT_2006_16_2_a3/
@article{JOLT_2006_16_2_a3,
author = {D. Ban},
title = {Symmetry of {Arthur} {Parameters} under {Aubert} {Involution}},
journal = {Journal of Lie Theory},
pages = {251--270},
year = {2006},
volume = {16},
number = {2},
zbl = {1102.22013},
url = {http://geodesic.mathdoc.fr/item/JOLT_2006_16_2_a3/}
}