### Abstract

Let G be a finite simple group of Lie type, and let π_{G} 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 π_{G}, unless G=PSU_{n}(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 language | English (US) |
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Pages (from-to) | 908-930 |

Number of pages | 23 |

Journal | Proceedings of the London Mathematical Society |

Volume | 106 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*106*(4), 908-930. https://doi.org/10.1112/plms/pds062

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

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 106, no. 4, pp. 908-930. https://doi.org/10.1112/plms/pds062

}

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 -