Representations of PGL(2) of a local field and harmonic forms on simplicial complexes

2007/01/11 by Paul Broussous, Broussous, Paul
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0701321

21 pages, 4 figures

arxiv created 2007/01/11 · arxiv updated 2009/12/01

Abstract

We give combinatorial models for complex, smooth, non-spherical, generic, irreducible representations of the group G=PGL(2,F), where F is a non-archimedean locally compact field. They use the graphs X_k lying above the tree of G, introduced in a previous work. We show that such representations may be realized as quotients of the cohomology of X_k for some k, or equivalently as spaces of discrete harmonic forms on X_k. For supercuspidal representations these models are unique.

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