Higher ramification and the local Langlands correspondence

• 成果类型: Article
• 署名作者: Bushnell, Colin J.; Henniart, Guy
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.3.5
• 发表日期: 2017
• 页码: 919-955
• 关键词: rankin-selberg convolutions; gl(n); REPRESENTATIONS; conductor; field

摘要

Let F be a non-Archimedean locally compact field. We show that the local Langlands correspondence over F has a strong property generalizing the higher ramification theorem of local class field theory. If pi is an irreducible cuspidal representation of a general linear group GL(n)(F) and sigma the corresponding irreducible representation of the Weil group W-F of F, the restriction of sigma to a ramification subgroup of W-F is determined by a truncation of the simple character theta(pi) contained in pi, and conversely. Numerical aspects of the relation are governed by a Herbrand-like function Psi(Theta) depending on the endo-class Theta of theta(pi). We give a method for calculating Psi(Theta) directly from Theta. Consequently, the ramification-theoretic structure of sigma can be predicted from the simple character theta(pi) alone.