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

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

doi:10.1112/plms/pds062

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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)
Pages (from-to)	908-930
Number of pages	23
Journal	Proceedings of the London Mathematical Society
Volume	106
Issue number	4
DOIs	https://doi.org/10.1112/plms/pds062
State	Published - Apr 2013

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/plms/pds062

Cite this

@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.\}",

note = "Funding Information: Received 19 March 2012; published online 9 November 2012. 2010 Mathematics Subject Classification 20B05, 20C05, 20C33, 20C15, 20D06. The third author is supported by the NSF (grants DMS-0901241 and DMS-1201374).",

year = "2013",

month = apr,

doi = "10.1112/plms/pds062",

language = "English (US)",

volume = "106",

pages = "908--930",

journal = "Proceedings of the London Mathematical Society",

issn = "0024-6115",

publisher = "John Wiley and Sons Ltd",

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.

N1 - Funding Information: Received 19 March 2012; published online 9 November 2012. 2010 Mathematics Subject Classification 20B05, 20C05, 20C33, 20C15, 20D06. The third author is supported by the NSF (grants DMS-0901241 and DMS-1201374).

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 - https://www.scopus.com/pages/publications/84877301202

UR - https://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

SN - 0024-6115

VL - 106

SP - 908

EP - 930

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 4

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this