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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
Front Cover for Irreducible Almost Simple Subgroups of Classical Algebraic Groups
Available Formats:
Electronic ISBN: 978-1-4704-2280-6
Product Code: MEMO/236/1114.E
110 pp 
List Price: $80.00
MAA Member Price: $72.00
AMS Member Price: $48.00
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  • Front Cover for Irreducible Almost Simple Subgroups of Classical Algebraic Groups
  • Back Cover for Irreducible Almost Simple Subgroups of Classical Algebraic Groups
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
110 pp 
List Price: $80.00
MAA Member Price: $72.00
AMS Member Price: $48.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2362015
    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.

  • Table of Contents
     
     
    • 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
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Volume: 2362015
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
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