Endo-parameters forp-adic classical groups

• 成果类型: Article
• 署名作者: Kurinczuk, Robert; Skodlerack, Daniel; Stevens, Shaun
• 署名单位: Imperial College London; ShanghaiTech University; University of East Anglia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00997-0
• 发表日期: 2021
• 页码: 597-723
• 关键词: supercuspidal representations; smooth representations; langlands correspondence; semisimple types; category; gl(n)(f); blocks

摘要

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are conjugate. This completes work of the first and third authors who showed that every irreducible cuspidal C-representation of a classical group is compactly induced from a cuspidal type. We generalize Bushnell and Henniart's notion of endo-equivalence to semisimple characters of general linear groups and to self-dual semisimple characters of classical groups, and introduce (self-dual) endo-parameters. We prove that these parametrize intertwining classes of (self-dual) semisimple characters and conjecture that they are in bijection with wild Langlands parameters, compatibly with the local Langlands correspondence.