eBook ISBN:  9781470422806 
Product Code:  MEMO/236/1114.E 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $48.00 
eBook ISBN:  9781470422806 
Product Code:  MEMO/236/1114.E 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $48.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 236; 2015; 110 ppMSC: 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 positivedimensional 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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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 positivedimensional 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