1.

Record Nr.

UNINA9910968798403321

Autore

Thomas Adam R

Titolo

The Irreducible Subgroups of Exceptional Algebraic Groups

Pubbl/distr/stampa

Providence : , : American Mathematical Society, , 2021

©2020

ISBN

9781470463458

1470463458

Edizione

[1st ed.]

Descrizione fisica

1 online resource (204 pages)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 1307

Classificazione

20G0520G1520G41

Disciplina

512.2

Soggetti

Linear algebraic groups

Representations of groups

Embeddings (Mathematics)

Maximal subgroups

Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory for linear algebraic groups

Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields

Group theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"November 2020, volume 268, number 1307 (fourth of 6 numbers)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Strategy for the proofs of theorems 5.1-9.1 -- Irreducible subgroups of G2 -- Irreducible subgroups of F4 -- Irreducible subgroups of G = E6 -- Irreducible subgroups of G = E7 -- Irreducible subgroups of G = E8 -- Corollaries -- Tables for theorem 1 -- Composition factors for G-irreducible subgroups -- Composition factors for the action of Levi subgroups.

Sommario/riassunto

"This monograph is a contribution to the study of the subgroup structure of exceptional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we complete the classification of irreducible connected subgroups of exceptional



algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected subgroup X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G"--