15 March 2023 The Steinberg representation is irreducible
Andrew Putman, Andrew Snowden
Author Affiliations +
Duke Math. J. 172(4): 775-808 (15 March 2023). 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.

Citation

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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

Information

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

Rights: Copyright © 2023 Duke University Press

Vol.172 • No. 4 • 15 March 2023
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