On the Moy–Prasad filtration

  • Jessica Fintzen

    University of Cambridge, UK; Duke University, Durham, USA
On the Moy–Prasad filtration cover
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Let KK be a maximal unramified extension of a non-archimedean local field with arbitrary residual characteristic pp. Let GG be a reductive group over KK which splits over a tamely ramified extension of KK. We show that the associated Moy–Prasad filtration representations are in a certain sense independent of pp. 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 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 pp to be large) and by Romano and the present author (which required GG to be absolutely simple and split). This yields new supercuspidal representations.

We also treat reductive groups GG that are not necessarily split over a tamely ramified field extension.

Cite this article

Jessica Fintzen, On the Moy–Prasad filtration. J. Eur. Math. Soc. 23 (2021), no. 12, pp. 4009–4063

DOI 10.4171/JEMS/1098