Cyclic diagrams and non-admissible irreducible representations of p-adic groups

Let F be a non-archimedean local field of residue characteristic p. The smooth representation theory of GL_2(F) over characteristic p fields is qualitatively different from that over the fields of other characteristics. For example, over coefficient fields of characteristic p, a compact induction from a compact open subgroup can have infinitely many supercuspidal quotients (after fixing a central character). Further, there exist irreducible representations of GL_2(F) which are not admissible. Such examples of representations for F unramified over Q_p were constructed by Breuil, Paskunas, and Le using the theory of diagrams. In this talk, we will consider a specific type of diagram, called cyclic diagram, which allows us to construct such examples for any local field F whose residue field properly contains F_p. This is based on joint work with Eknath Ghate and Daniel Le.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062