2016/10/21 by Elmar Große-Klönne, Elmar Grosse-Klönne
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Finite Group Theory Research #Mathematics #Pure mathematics #math.NT
paper · pdf · doi:10.1093/imrn/rnw257
published as International Mathematical Research Notices 2018, Issue 3, 862--906 (2018) · International Mathematics Research Notices
openalex publication_date 2016/10/21 · arxiv created 2017/01/03 · arxiv updated 2018/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let |\mathfrak o| be the ring of integers in a finite extension field of |\mathbb Qp|, let |k| be its residue field. Let |G| be a split reductive group over |\mathbb Qp|, let |\mathcal H(G,I0)| be its pro-|p| Iwahori–Hecke |\mathfrak o|-algebra. In [2] we introduced a general principle how to assign to a certain additionally chosen datum |(C(\bullet),φ,τ)| an exact functor |M↦\bf D(Θ_*\mathcal VM)| from finite length |\mathcal H(G,I0)|-modules to |(φr,Γ)|-modules. In this paper we concretely work out such data |(C(\bullet),φ,τ)| for the classical matrix groups. We show that the corresponding functor identifies the set of (standard) supersingular |\mathcal H(G,I0)⊗_\mathfrak ok|-modules with the set of |(φr,Γ)|-modules satisfying a certain symmetry condition.