Endo-parameters for p-adic Classical Groups

Robert Kurinczuk, Daniel Skodlerack, Shaun Stevens

Research output: Contribution to journalArticle

3 Citations (Scopus)
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Abstract

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.

Original languageEnglish
Pages (from-to)597–723
Number of pages127
JournalInventiones Mathematicae
Volume223
Issue number2
Early online date21 Sep 2020
DOIs
Publication statusPublished - Feb 2021

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