Irreducible Almost Simple Subgroups of Classical Algebraic Groups (Memoirs of the American Mathematical Society) - Softcover

Burness, Timothy C.; Ghandour, Soumaia; Marion, Claude; Testerman, Donna M.

Softcover

ISBN 10: 147041046X ISBN 13: 9781470410469

Publisher: American Mathematical Society, 2015

Synopsis

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.

About this title

About the Author

Timothy C. Burness, University of Bristol, United Kingdom.

Soumaia Ghandour, Lebanese University, Nabatieh, Lebanon.

Claude Marion, University of Fribourg, Switzerland.

Donna M. Testerman, Ecole Polytechnique Federale de Lausanne, Switzerland.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2015
• Language: English
• ISBN 10: 147041046X
• ISBN 13: 9781470410469
• Binding: Paperback
• Number of pages: 110