arXiv Analytics

Sign in

arXiv:math/0701321 [math.RT]AbstractReferencesReviewsResources

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

Paul Broussous

Published 2007-01-11Version 1

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.

Related articles: Most relevant | Search more
arXiv:0708.2636 [math.RT] (Published 2007-08-20)
Genericity of supercuspidal representations of p-adic Sp(4)
arXiv:math/0409543 [math.RT] (Published 2004-09-28, updated 2005-09-11)
Algebraic groups over a 2-dimensional local field: irreducibility of certain induced representations
arXiv:1003.2742 [math.RT] (Published 2010-03-13)
Representations of unipotent groups over local fields and Gutkin's conjecture