On e-local structures for ℤ_ℓ-spetses

2024/08/12 by Damiano Rossi, Rossi, Damiano, Jason Semeraro +1
Mathematics · #20C15 #55P10 #55R35 #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Group Theory (math.GR) #Holomorphic and Operator Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.06132

openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime power, ℓ a prime not dividing q, and e the order of q modulo ℓ. We show that the geometric realisation of the nerve of the transporter category of e-split Levi subgroups of a finite reductive group G over \mathbbF_q is homotopy equivalent to the classifying space BG up to ℓ-completion. We suggest a generalisation of this equivalence to the setting of ℤ_ℓ-reflection cosets and establish a related fact involving the associated orbit spaces. We also establish a Dade-like formula for unipotent characters of ℤ_ℓ-spetses inspired by a question of Broué.

Related

• Partial character tables for ℤ_ℓ-spetses
• A 2-compact group as a spets
• Sects
• Specialization of F-Zips
• The Brown complex in non-defining characteristic and applications