The irreducible subgroups of exceptional algebraic groups / Adam R. Thomas.

Format:

Book

Author/Creator:

Thomas, Adam R., 1988- author.

Series:

Memoirs of the American Mathematical Society ; v. 1307.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1307

Language:

English

Subjects (All):

Linear algebraic groups.

Representations of groups.

Embeddings (Mathematics).

Maximal subgroups.

Physical Description:

1 online resource (pages cm.)

Place of Publication:

Providence, RI : American Mathematical Society, [2021]

System Details:

Mode of access : World Wide Web

text file

Summary:

"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"-- Provided by publisher.

Contents:

1. Introduction 2. Notation 3. Preliminaries 4. Strategy for the proofs of Theorems - 5. Irreducible subgroups of $G_2$ 6. Irreducible subgroups of $F_4$ 7. Irreducible subgroups of $G = E_6$ 8. Irreducible subgroups of $G = E_7$ 9. Irreducible subgroups of $G = E_8$ 10. Corollaries 11. Tables for Theorem 12. Composition factors for $G$-irreducible subgroups 13. Composition factors for the action of Levi subgroups

Notes:

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

Includes bibliographical references.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2020

Description based on print version record.

Other Format:

Print version: Thomas, Adam R., 1988- irreducible subgroups of exceptional algebraic groups /

ISBN:

9781470463458

Access Restriction:

Restricted for use by site license.