Rational G-spectra for rank 2 toral groups of mixed type

2025/01/26 by J. P. C. Greenlees, Greenlees, J. P. C. · 2 citations
Mathematics · #55P42 #55P91 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2501.15584

openalex publication_date 2025/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit and calculable algebraic model for the block of rational G-spectra on full subgroups when G has identity component a 2-torus T, and component group of order 2 acting non-trivially on H₁(T). The example of particular interest is the normalizer of the maximal torus in U(2), which constitutes one of the most complicated blocks in the analysis of SU(3). This builds on the determination of subgroups up to conjugacy in arXiv 2501.06914

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• The spectral space of conjugacy classes of subgroups of a compact Lie group
• Rational G-spectra over blocks with finite Weyl groups

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