Journal of Lie Theory

no. 2
Symmetry of Arthur Parameters under Aubert Involution
Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 251-270
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.
DOI: 10.5802/jolt.409
Classification: 22E50, 11F70
Keywords: Arthur parameters, Aubert involution, odd orthogonal groups over $p$-adic fields 
@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},
     doi = {10.5802/jolt.409},
     zbl = {1102.22013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.409/}
}
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%A D. Ban
%T Symmetry of Arthur Parameters under Aubert Involution
%J Journal of Lie Theory
%D 2006
%P 251-270
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%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.409/
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D. Ban. Symmetry of Arthur Parameters under Aubert Involution. Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 251-270. doi: 10.5802/jolt.409

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