On certain Iwahori--Hecke modules of $GL_3$ in characteristic $p$

Peng Xu

paper

On certain Iwahori--Hecke modules of $G L_{3}$ in characteristic $p$

arXiv:1902.02151

Abstract

In this note, we show that the natural analogue of certain finiteness result of Barthel--Livn $e ˊ$ on $G L_{2}$ fails for $G L_{3}$ . More precisely, within the pro- $p$ -Iwahori invariants of a maximal compact induction of $G L_{3}$ , we show there exist non-zero Iwahori--Hecke submodules of \emph{infinite} codimension.

Enlarged and revised version. Comments are welcome

On certain Iwahori--Hecke modules of GL3​ in characteristic p

Abstract

On certain Iwahori--Hecke modules of $G L_{3}$ in characteristic $p$