Irreducible geometric subgroups of classical algebraic groups

Tim C Burness; Soumaia Ghandour; Donna M Testerman

doi:10.1090/memo/1130

Irreducible geometric subgroups of classical algebraic groups

Tim C Burness, Soumaia Ghandour, Donna M Testerman

Research output: Contribution to journal › Article (Academic Journal) › peer-review

233 Downloads (Pure)

Abstract

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper we classify all such triples $(G,H,V)$, where $H$ is a maximal closed disconnected positive-dimensional subgroup of $G$, and $H$ preserves a natural geometric structure on $W$.

Original language	English
Article number	1130
Number of pages	100
Journal	Memoirs of the American Mathematical Society
Volume	239
Issue number	1130
Early online date	9 Jun 2015
DOIs	https://doi.org/10.1090/memo/1130
Publication status	Published - 2016

Access to Document

10.1090/memo/1130Licence: CC BY-NC

2016 Irreducible geometric subgroups of classical algebraic groups
This is the final published version of the article (version of record). It first appeared online via AMS at http://dx.doi.org/10.1090/memo/1130 . Please refer to any applicable terms of use of the publisher.
Final published version, 1.01 MBLicence: CC BY-NC

Fingerprint Dive into the research topics of 'Irreducible geometric subgroups of classical algebraic groups'. Together they form a unique fingerprint.

Dr Tim C Burness
- t.burness@bristol.ac.uk
- School of Mathematics - Reader in Pure Mathematics
- Pure Mathematics
- Algebra
Person: Academic , Member

Cite this

@article{3c640cf8ba434928a208d067d6d198f4,

title = "Irreducible geometric subgroups of classical algebraic groups",

abstract = "Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper we classify all such triples $(G,H,V)$, where $H$ is a maximal closed disconnected positive-dimensional subgroup of $G$, and $H$ preserves a natural geometric structure on $W$.",

author = "Burness, {Tim C} and Soumaia Ghandour and Testerman, {Donna M}",

year = "2016",

doi = "10.1090/memo/1130",

language = "English",

volume = "239",

journal = "Memoirs of the American Mathematical Society",

issn = "0065-9266",

publisher = "American Mathematical Society",

number = "1130",

}

TY - JOUR

T1 - Irreducible geometric subgroups of classical algebraic groups

AU - Burness, Tim C

AU - Ghandour, Soumaia

AU - Testerman, Donna M

PY - 2016

Y1 - 2016

N2 - Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper we classify all such triples $(G,H,V)$, where $H$ is a maximal closed disconnected positive-dimensional subgroup of $G$, and $H$ preserves a natural geometric structure on $W$.

AB - Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper we classify all such triples $(G,H,V)$, where $H$ is a maximal closed disconnected positive-dimensional subgroup of $G$, and $H$ preserves a natural geometric structure on $W$.

U2 - 10.1090/memo/1130

DO - 10.1090/memo/1130

M3 - Article (Academic Journal)

VL - 239

JO - Memoirs of the American Mathematical Society

JF - Memoirs of the American Mathematical Society

SN - 0065-9266

IS - 1130

M1 - 1130

ER -

Irreducible geometric subgroups of classical algebraic groups

Abstract

Access to Document

Dr Tim C Burness

Cite this