English

The Steinberg representation is irreducible

Representation Theory 2023-04-04 v3 Group Theory

Abstract

We prove that the Steinberg representation of a connected reductive group over an infinite field is irreducible. For finite fields, this is a classical theorem of Steinberg and Curtis.

Keywords

Cite

@article{arxiv.2107.00794,
  title  = {The Steinberg representation is irreducible},
  author = {Andrew Putman and Andrew Snowden},
  journal= {arXiv preprint arXiv:2107.00794},
  year   = {2023}
}

Comments

28 pages, major revision, to appear in Duke Math. J

R2 v1 2026-06-24T03:49:37.405Z