Irreducible Almost Simple Subgroups of Classical Algebraic Groups

ISBN-13: 9781470410469 / Angielski

Timothy C. Burness;Soumaia Ghandour;Claude Marion

Opis

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $pgeq 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a nontrivial $p$-restricted irreducible tensor indecomposable rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper the authors classify the triples $(G,H,V)$ of this form, where $V eq W,W^{*}$ and $H$ is a disconnected almost simple positive-dimensional closed subgroup of $G$ acting irreducibly on $W$. Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples $(G,H,V)$ where $G$ is a simple algebraic group over $K$, and $H$ is a maximal closed subgroup of positive dimension.

Spis treści

• Introduction
• Preliminaries
• The case $H^0 = A_m$
• The case $H^0=D_m$, $m \ge 5$
• The case $H^0=E_6$
• The case $H^0 = D_4$
• Proof of Theorem 5
• Notation
• Bibliography