Stable vectors in Moy-Prasad filtrations

Author: 

Fintzen, J
Romano, B

Publication Date: 

9 February 2017

Journal: 

Compositio Mathematica

Last Updated: 

2021-04-10T00:07:11.63+01:00

Issue: 

2

Volume: 

153

DOI: 

10.1112/S0010437X16008228

page: 

358-372

abstract: 

Let k be a finite extension of Qp , let G be an absolutely simple split reductive group over k , and let K be a maximal unramified extension of k . To each point in the Bruhat–Tits building of GK , Moy and Prasad have attached a filtration of G(K) by bounded subgroups. In this paper we give necessary and sufficient conditions for the dual of the first Moy–Prasad filtration quotient to contain stable vectors for the action of the reductive quotient. Our work extends earlier results by Reeder and Yu, who gave a classification in the case when p is sufficiently large. By passing to a finite unramified extension of k if necessary, we obtain new supercuspidal representations of G(k).

Symplectic id: 

1115295

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article