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

Peng Xu

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

Representation Theory 2020-04-08 v2

Authors: Peng Xu

Abstract

In this note, we show that the natural analogue of certain finiteness result of Barthel--Livn $\acute{\text{e}}$ on $GL_2$ fails for $GL_3$ . More precisely, within the pro- $p$ -Iwahori invariants of a maximal compact induction of $GL_3$ , we show there exist non-zero Iwahori--Hecke submodules of \emph{infinite} codimension.

Keywords

iwahori-hecke modules gl_3 characteristic p pro-p-ihara invariants finite codimension maximal compact induction

Cite

@article{arxiv.1902.02151,
  title  = {On certain Iwahori--Hecke modules of $GL_3$ in characteristic $p$},
  author = {Peng Xu},
  journal= {arXiv preprint arXiv:1902.02151},
  year   = {2020}
}

Comments

Enlarged and revised version. Comments are welcome

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