An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Timothy C. Burness University of Bristol, Bristol, United Kingdom
Soumaïa Ghandour Lebanese University, Nabatieh, Lebanon
Claude Marion University of Fribourg, Fribourg, Switzerland
Donna M. Testerman École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
Available Formats:
Electronic ISBN: 978-1-4704-2280-6
Product Code: MEMO/236/1114.E
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $48.00 Click above image for expanded view Irreducible Almost Simple Subgroups of Classical Algebraic Groups Timothy C. Burness University of Bristol, Bristol, United Kingdom Soumaïa Ghandour Lebanese University, Nabatieh, Lebanon Claude Marion University of Fribourg, Fribourg, Switzerland Donna M. Testerman École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Available Formats:  Electronic ISBN: 978-1-4704-2280-6 Product Code: MEMO/236/1114.E  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$48.00
• Book Details

Memoirs of the American Mathematical Society
Volume: 2362015; 110 pp
MSC: Primary 20;

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p\geq 0$ 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 $V \neq W,W^{*}$ 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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. The case $H^0 = A_m$
• 4. The case $H^0=D_m$, $m \ge 5$
• 5. The case $H^0=E_6$
• 6. The case $H^0 = D_4$
• 7. Proof of Theorem
• Notation
• Request Review Copy
• Get Permissions
Volume: 2362015; 110 pp
MSC: Primary 20;

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p\geq 0$ 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 $V \neq W,W^{*}$ 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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. The case $H^0 = A_m$
• 4. The case $H^0=D_m$, $m \ge 5$
• 5. The case $H^0=E_6$
• 6. The case $H^0 = D_4$
• 7. Proof of Theorem
• Notation
Please select which format for which you are requesting permissions.