当前位置: X-MOL 学术J. Number Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
R-groups for unitary principal series of Spin groups
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-02-23 , DOI: 10.1016/j.jnt.2021.01.017
Dubravka Ban , Kwangho Choiy , David Goldberg

We study the unitary principal series of the split group Spinm(F), where F is a p-adic field. Let χ˜ be a unitary character of a maximal F-split torus T˜ of GSpinm(F), and let χ be its restriction to T=T˜Spinm(F). The R-groups Rχ˜ and Rχ of the corresponding principal series representations fit in the exact sequence 0Rχ˜RχRχ/Rχ˜0. We give a complete answer to the question of splitting of this exact sequence. We also prove that the multiplicity is one when irreducible constituents in unitary principal series are restricted from GSpin(F) to Spin(F). Further, based on Keys' result, we prove Arthur's conjecture on R-groups for unitary principal series of Spin.



中文翻译:

自旋群的单一主系列的R-

我们研究分裂组的一元本因级数 小号p一世ñF,其中Fp- adic字段。让χ是最大F分裂环面的单一特征ŤG小号p一世ñF,令χ为它对Ť=Ť小号p一世ñF。在[R -groups[Rχ[Rχ 相应的主系列表示形式中的一个按精确顺序拟合 0[Rχ[Rχ[Rχ/[Rχ0。对于这个精确序列的分割问题,我们给出了完整的答案。我们还证明了,当单一主体级数中的不可约成分被限制于G小号p一世ñF小号p一世ñF。此外,根据Keys的结果,我们证明了Arthur关于R的unit-群的猜想。小号p一世ñ

更新日期:2021-03-16
down
wechat
bug