具有自同构的根系的对偶及其在非分裂群中的应用
Dualities for root systems with automorphisms and applications to non-split groups
摘要：
本文建立了具有自同构的根系的一些初等对偶。本文给出了非阿基米德局部域上约化群的几个应用：（1）证明了Pappas-Rapoport-Smithling关于一般不可裂群上的$\{ μ\}$ -容许集的极值元的猜想;（2）对于拟分裂群，给出了Bruhat-Tits échelonnage根系$Σ_0$，Knop根系$\widetildeΣ_0$，和Macdonald根系$Φ$，（3）对于拟分裂群，构造了仿射Hecke代数的中心的几何基，并给出了稳定Bernstein中心的某些重要元素在此基上的表示.
英文摘要：
This article establishes some elementary dualities for root systems with automorphisms. We give several applications to reductive groups over nonarchimedean local fields: (1) the proof of a conjecture of Pappas-Rapoport-Smithling characterizing the extremal elements of the $\{ μ\}$-admissible sets attached to general non-split groups; (2) for quasi-split groups, a simple uniform description of the Bruhat-Tits échelonnage root system $Σ_0$, the Knop root system $\widetildeΣ_0$, and the Macdonald root system $Σ_1$, in terms of Galois actions on the absolute roots $Φ$; and (3) for quasi-split groups, the construction of the geometric basis of the center of a parahoric Hecke algebra, and the expression of certain important elements of the stable Bernstein center in terms of this basis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
