Representations of the general linear groups which are irreducible over subgroups

Alexander S. Kleshchev; Pham Huu Tiep

doi:10.1353/ajm.0.0108

Representations of the general linear groups which are irreducible over subgroups

Alexander S. Kleshchev
, Pham Huu Tiep

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

17 Scopus citations

Abstract

We classify all triples (G, V,H) such that SL_n(q) ≤ G ≤ GL_n(q), V is a representation of G of dimension greater than one over an algebraically closed field F of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓_H is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.

Original language	English (US)
Pages (from-to)	425-473
Number of pages	49
Journal	American Journal of Mathematics
Volume	132
Issue number	2
DOIs	https://doi.org/10.1353/ajm.0.0108
State	Published - Apr 2010
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1353/ajm.0.0108

Cite this

@article{3ff19019aa774f7cb0b973501e36324d,

title = "Representations of the general linear groups which are irreducible over subgroups",

abstract = "We classify all triples (G, V,H) such that SLn(q) ≤ G ≤ GLn(q), V is a representation of G of dimension greater than one over an algebraically closed field F of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓H is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.",

author = "Kleshchev, \{Alexander S.\} and Tiep, \{Pham Huu\}",

year = "2010",

month = apr,

doi = "10.1353/ajm.0.0108",

language = "English (US)",

volume = "132",

pages = "425--473",

journal = "American Journal of Mathematics",

issn = "0002-9327",

publisher = "Johns Hopkins University Press",

number = "2",

}

TY - JOUR

T1 - Representations of the general linear groups which are irreducible over subgroups

AU - Kleshchev, Alexander S.

AU - Tiep, Pham Huu

PY - 2010/4

Y1 - 2010/4

N2 - We classify all triples (G, V,H) such that SLn(q) ≤ G ≤ GLn(q), V is a representation of G of dimension greater than one over an algebraically closed field F of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓H is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.

AB - We classify all triples (G, V,H) such that SLn(q) ≤ G ≤ GLn(q), V is a representation of G of dimension greater than one over an algebraically closed field F of characteristic prime to q, and H is a proper subgroup of G such that the restriction V↓H is irreducible. This problem is a natural part of the Aschbacher-Scott program on maximal subgroups in finite classical groups.

UR - https://www.scopus.com/pages/publications/77951061685

UR - https://www.scopus.com/pages/publications/77951061685#tab=citedBy

U2 - 10.1353/ajm.0.0108

DO - 10.1353/ajm.0.0108

M3 - Article

AN - SCOPUS:77951061685

SN - 0002-9327

VL - 132

SP - 425

EP - 473

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 2

ER -

Representations of the general linear groups which are irreducible over subgroups

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this