Representations of finite special linear groups in non-defining characteristic

Alexander S. Kleshchev; Pham Huu Tiep

doi:10.1016/j.aim.2008.09.011

Representations of finite special linear groups in non-defining characteristic

Alexander S. Kleshchev, Pham Huu Tiep

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

27 Scopus citations

Abstract

We classify irreducible modules over the finite special linear group SL_n (q) in the non-defining characteristic ℓ, describe restrictions of irreducible modules from GL_n (q) to SL_n (q), classify complex irreducible characters of SL_n (q) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SL_n (q).

Original language	English (US)
Pages (from-to)	478-504
Number of pages	27
Journal	Advances in Mathematics
Volume	220
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2008.09.011
State	Published - Jan 30 2009
Externally published	Yes

Keywords

Finite special linear group
Group theory
Modular representation theory

ASJC Scopus subject areas

Mathematics(all)

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10.1016/j.aim.2008.09.011

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title = "Representations of finite special linear groups in non-defining characteristic",

abstract = "We classify irreducible modules over the finite special linear group SLn (q) in the non-defining characteristic ℓ, describe restrictions of irreducible modules from GLn (q) to SLn (q), classify complex irreducible characters of SLn (q) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SLn (q).",

keywords = "Finite special linear group, Group theory, Modular representation theory",

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

note = "Funding Information: ✩ Research supported by the NSF (grants DMS-0654147 and DMS-0600967). This work was completed when both authors visited MSRI, whom we thank for support. * Corresponding author. E-mail addresses: klesh@uoregon.edu (A.S. Kleshchev), tiep@math.arizona.edu (P.H. Tiep). 1 Present address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.",

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T1 - Representations of finite special linear groups in non-defining characteristic

AU - Kleshchev, Alexander S.

AU - Tiep, Pham Huu

N1 - Funding Information: ✩ Research supported by the NSF (grants DMS-0654147 and DMS-0600967). This work was completed when both authors visited MSRI, whom we thank for support. * Corresponding author. E-mail addresses: klesh@uoregon.edu (A.S. Kleshchev), tiep@math.arizona.edu (P.H. Tiep). 1 Present address: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA.

PY - 2009/1/30

Y1 - 2009/1/30

N2 - We classify irreducible modules over the finite special linear group SLn (q) in the non-defining characteristic ℓ, describe restrictions of irreducible modules from GLn (q) to SLn (q), classify complex irreducible characters of SLn (q) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SLn (q).

AB - We classify irreducible modules over the finite special linear group SLn (q) in the non-defining characteristic ℓ, describe restrictions of irreducible modules from GLn (q) to SLn (q), classify complex irreducible characters of SLn (q) irreducible modulo l, and discuss unitriangularity of the l-decomposition matrix for SLn (q).

KW - Finite special linear group

KW - Group theory

KW - Modular representation theory

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EP - 504

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 2

ER -

Representations of finite special linear groups in non-defining characteristic

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Keywords

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