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Representations of PGL ( 2 ) of a local field and harmonic cochains on graph

Paul Broussous (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We give combinatorial models for non-spherical, generic, smooth, complex representations of the group G = PGL ( 2 , F ) , where F is a non-Archimedean locally compact field. More precisely we carry on studying the graphs ( X ˜ k ) k 0 defined in a previous work. We show that such representations may be obtained as quotients of the cohomology of a graph X ˜ k , for a suitable integer k , or equivalently as subspaces of the space of discrete harmonic cochains on such a graph. Moreover, for supercuspidal representations, these models...

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