On the Moy-Prasad filtration

2015/11/02 by Fintzen, Jessica
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1511.00726

Abstract

Let K be a maximal unramified extension of a nonarchimedean local field with arbitrary residual characteristic p. Let G be a reductive group over K which splits over a tamely ramified extension of K. We show that the associated Moy-Prasad filtration representations are in a certain sense independent of p. We also establish descriptions of these representations in terms of explicit Weyl modules and as representations occurring in a generalized Vinberg-Levy theory. As an application, we use these results to provide necessary and sufficient conditions for the existence of stable vectors in Moy-Prasad filtration representations, which extend earlier results by Reeder and Yu (which required p to be large) and by Romano and the author (which required G to be absolutely simple and split). This yields new supercuspidal representations. We also treat reductive groups G that are not necessarily split over a tamely ramified field extension.

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