Pictures of compact Lie groups (after Serre)

2022/11/02 by Skip Garibaldi, Garibaldi, Skip
Mathematics · #22C05 #22E47 (Secondary) #22G20 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.00862

openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp(2n), the picture generated by the method is connected with abelian varieties over a number field or a finite field. We follow the procedure to produce pictures for the three simply connected simple groups of rank 2. The pictures for two of these have previously been discussed in the literature in a different setting. The remaining one, type G₂, has the most complicated picture.

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