Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type

Gerhard Heide, Jan Saxl, Pham Huu Tiep, Alexandre E. Zalesski

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n≥3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.

Original languageEnglish (US)
Pages (from-to)908-930
Number of pages23
JournalProceedings of the London Mathematical Society
Volume106
Issue number4
DOIs
StatePublished - Apr 2013

Fingerprint

Groups of Lie Type
Induced Representations
Conjugacy
Simple group
Irreducible Representation
Permutation Representation
Finite Simple Group
Coprime
Conjugation
Exception
Tensor

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type. / Heide, Gerhard; Saxl, Jan; Tiep, Pham Huu; Zalesski, Alexandre E.

In: Proceedings of the London Mathematical Society, Vol. 106, No. 4, 04.2013, p. 908-930.

Research output: Contribution to journalArticle

@article{fc186ce841b945b597e363e941c3c425,
title = "Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type",
abstract = "Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n≥3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.",
author = "Gerhard Heide and Jan Saxl and Tiep, {Pham Huu} and Zalesski, {Alexandre E.}",
year = "2013",
month = "4",
doi = "10.1112/plms/pds062",
language = "English (US)",
volume = "106",
pages = "908--930",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "4",

}

TY - JOUR

T1 - Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type

AU - Heide, Gerhard

AU - Saxl, Jan

AU - Tiep, Pham Huu

AU - Zalesski, Alexandre E.

PY - 2013/4

Y1 - 2013/4

N2 - Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n≥3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.

AB - Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n≥3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.

UR - http://www.scopus.com/inward/record.url?scp=84877301202&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84877301202&partnerID=8YFLogxK

U2 - 10.1112/plms/pds062

DO - 10.1112/plms/pds062

M3 - Article

AN - SCOPUS:84877301202

VL - 106

SP - 908

EP - 930

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 4

ER -