Reducible subgroups of exceptional algebraic groups

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Reducible subgroups of exceptional algebraic groups. / Litterick, Alastair; Thomas, Adam.

In: Journal of Pure and Applied Algebra, Vol. 223, No. 6, 01.06.2019, p. 2489-2529.

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Litterick, Alastair ; Thomas, Adam. / Reducible subgroups of exceptional algebraic groups. In: Journal of Pure and Applied Algebra. 2019 ; Vol. 223, No. 6. pp. 2489-2529.

Bibtex

@article{1814fea9611a49918fe3e9a04ebdf4a1,
title = "Reducible subgroups of exceptional algebraic groups",
abstract = "Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected Gcr subgroups when G has exceptional type, by determining the L0-irreducible connected reductive subgroups for each simple classical factor L0 of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type F4 and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere. ",
author = "Alastair Litterick and Adam Thomas",
year = "2019",
month = jun,
day = "1",
doi = "10.1016/j.jpaa.2018.09.004",
language = "English",
volume = "223",
pages = "2489--2529",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "6",

}

RIS

TY - JOUR

T1 - Reducible subgroups of exceptional algebraic groups

AU - Litterick, Alastair

AU - Thomas, Adam

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected Gcr subgroups when G has exceptional type, by determining the L0-irreducible connected reductive subgroups for each simple classical factor L0 of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type F4 and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere.

AB - Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected Gcr subgroups when G has exceptional type, by determining the L0-irreducible connected reductive subgroups for each simple classical factor L0 of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type F4 and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere.

U2 - 10.1016/j.jpaa.2018.09.004

DO - 10.1016/j.jpaa.2018.09.004

M3 - Article

VL - 223

SP - 2489

EP - 2529

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 6

ER -