Representations with unipotent reduction for \(\operatorname{SO}(2n+1)\). II: Endoscopy. (Représentations de réduction unipotente pour \(\operatorname{SO}(2n+1)\). II: Endoscopie.) (French. English summary) Zbl 1415.22013
Let \(F\) be a non-archimedean field of characteristic 0 and fix \(n \ge 1\). Consider, for each of the two forms of \(\text{SO}(2n+1)\) over \(F\), the tempered representations of unipotent reduction of \(\text{SO}(2n+1,F)\). In the present article it is proved that Lusztig’s parametrisation of these representations satisfies the expected conditions regarding endoscopic transfer. The article is a continuation of the author’s work [J. Lie Theory 28, No. 2, 381–426 (2018; Zbl 1416.22019)]. The proof follows the lines of C. Mœglin and the author [Invent. Math. 152, No. 3, 461–623 (2003; Zbl 1037.22036)], where also some of the computations needed in the present paper have been done.
The theorem is derived from a result on the transfer of functions stated as Proposition 1.2. Using the cited articles the transfer of elliptic representations is obtained from Proposition 1.2.
Proposition 1.2 is proved via transfer for Lie algebras by computing explicitly the Fourier transform of certain orbital integrals.
The theorem is derived from a result on the transfer of functions stated as Proposition 1.2. Using the cited articles the transfer of elliptic representations is obtained from Proposition 1.2.
Proposition 1.2 is proved via transfer for Lie algebras by computing explicitly the Fourier transform of certain orbital integrals.
Reviewer: J. G. M. Mars (Utrecht)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
References:
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