Skip to main content

On the Moy-Prasad filtration

Publication ,  Journal Article
Fintzen, J
Published in: Journal of the European Mathematical Society
January 1, 2021

Let K be a maximal unramified extension of a non-archimedean 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 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 present 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.

Duke Scholars

Published In

Journal of the European Mathematical Society

DOI

ISSN

1435-9855

Publication Date

January 1, 2021

Volume

23

Issue

12

Start / End Page

4009 / 4063

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Fintzen, J. (2021). On the Moy-Prasad filtration. Journal of the European Mathematical Society, 23(12), 4009–4063. https://doi.org/10.4171/JEMS/1098
Fintzen, J. “On the Moy-Prasad filtration.” Journal of the European Mathematical Society 23, no. 12 (January 1, 2021): 4009–63. https://doi.org/10.4171/JEMS/1098.
Fintzen J. On the Moy-Prasad filtration. Journal of the European Mathematical Society. 2021 Jan 1;23(12):4009–63.
Fintzen, J. “On the Moy-Prasad filtration.” Journal of the European Mathematical Society, vol. 23, no. 12, Jan. 2021, pp. 4009–63. Scopus, doi:10.4171/JEMS/1098.
Fintzen J. On the Moy-Prasad filtration. Journal of the European Mathematical Society. 2021 Jan 1;23(12):4009–4063.

Published In

Journal of the European Mathematical Society

DOI

ISSN

1435-9855

Publication Date

January 1, 2021

Volume

23

Issue

12

Start / End Page

4009 / 4063

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics