Cocompact lattices of minimal covolume in rank 2 Kac-Moody groups, Part II

2010/05/31 by Inna, Capdeboscq, Anne Thomas +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1005.5702

openalex publication_date 2010/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a topological Kac-Moody group of rank 2 with symmetric Cartan matrix, defined over a finite field F_q. An example is G = SL(2,F_q((t^-1))). We determine a positive lower bound on the covolumes of cocompact lattices in G, and construct a cocompact lattice Γ₀ < G which realises this minimum. This completes the work begun in Part I, which considered the cases when G admits an edge-transitive lattice.

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