Journal of Lie Theory

no. 2
Représentations de Réduction Unipotente pour SO(2n+1), I: une Involution
Jean-Loup Waldspurger1
1IMJ-PRG CNRS, 4 place Jussieu, 75005 Paris, France
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 381-426
We consider a group SO(2n+1) over a p-adic field and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined an involution in the complex vector space generated by those representations which are elliptic. It is strongly related to another involution defined by Lusztig for finite groups. We give a new definition of our involution and we prove it commutes, in some sense, with Jacquet functor.
DOI: 10.5802/jolt.1007
Classification: 22E50
Keywords: Representations of unipotent reduction, endoscopy

Jean-Loup Waldspurger  1

1 IMJ-PRG CNRS, 4 place Jussieu, 75005 Paris, France 
Jean-Loup Waldspurger. Représentations de Réduction Unipotente pour SO(2n+1), I: une Involution. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 381-426. doi: 10.5802/jolt.1007
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     author = {Jean-Loup Waldspurger},
     title = {Repr\'esentations de {R\'eduction} {Unipotente} pour {SO(2n+1),} {I:} une {Involution}},
     journal = {Journal of Lie Theory},
     pages = {381--426},
     year = {2018},
     volume = {28},
     number = {2},
     doi = {10.5802/jolt.1007},
     zbl = {1416.22019},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1007/}
}
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