The Steinberg representation is irreducible

Andrew Putman; Andrew Snowden

doi:10.1215/00127094-2022-0016

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.

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Andrew Putman. Andrew Snowden. "The Steinberg representation is irreducible." Duke Math. J. 172 (4) 775 - 808, 15 March 2023. https://doi.org/10.1215/00127094-2022-0016

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Received: 29 July 2021; Revised: 18 February 2022; Published: 15 March 2023

First available in Project Euclid: 20 February 2023

MathSciNet: MR4557760

zbMATH: 07684351

Digital Object Identifier: 10.1215/00127094-2022-0016

Subjects:

Primary: 16S34

Secondary: 20E42 , 20F18

Keywords: reductive groups , representation theory , Steinberg representation , Tits building

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