Types for tame p-adic groups

• 成果类型: Article
• 署名作者: Fintzen, Jessica
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.193.1.4
• 发表日期: 2021
• 页码: 303-346
• 关键词: supercuspidal representations; semisimple types; k-types

摘要

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we show that every smooth irreducible complex representation of G(k) contains an .6-type of the form constructed by Kim-Yu and that every irreducible supercuspidal representation arises from Yu's construction. This improves an earlier result of Kim, which held only in characteristic zero and with a very large and ineffective bound on p. By contrast, our bound on p is explicit and tight, and our result holds in positive characteristic as well. Moreover, our approach is more explicit in extracting an input for Yu's construction from a given representation.