Representations of PGL(2) of a local field and harmonic forms on simplicial complexes
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 Xk 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 Xk for some k, or equivalently as spaces of discrete harmonic forms on Xk. For supercuspidal representations these models are unique.
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