A fixed point theorem for the action of SL_n over local fields on symmetric spaces of infinite dimension and finite rank

2025/05/08 by Viola, Federico · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.05220

Abstract

Let F be a non-archimedean local field, and let G = SL_n(F), n ≥ 3. Let X be an infinite-dimensional simply connected symmetric space of finite rank, with nonpositive curvature operator. We prove that every continuous action by isometries of G on X has a fixed point.

Citations

• Irreducible finite-index representations of automorphism groups of trees
• The Zeta Functions of Complexes from \Sp(4)
• Expanders and the Affine Building of \rm Sp_n
• The de Rham decomposition theorem for metric spaces
• Centers of convex subsets of buildings

Cited by

• Irreducible finite-index representations of automorphism groups of trees

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