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Irreducible almost simple subgroups of classical algebraic groups

Irreducible almost simple subgroups of classical algebraic groups
Irreducible almost simple subgroups of classical algebraic groups
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p ? 0 with natural module W. Let H be a closed subgroup of G and let V be a nontrivial irreducible tensor indecomposable -restricted rational KG-module such that the restriction of V to H is irreducible. In this paper we classify the triples (G,H,V ) of this form, where H is a closed disconnected almost simple positive-dimensional subgroup of G acting irreducibly on W. Moreover, by combining this result with earlier work, we complete the classifcation 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.
1-84
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Ghandour, Soumaia
575259be-059d-41cb-8291-2314325e3a91
Marion, Claude
a48acc05-e3ed-4a6d-b237-ecd76d719c9e
Testerman, Donna M.
5d6fe188-b3e7-45cd-b332-5c8ae7093c63
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Ghandour, Soumaia
575259be-059d-41cb-8291-2314325e3a91
Marion, Claude
a48acc05-e3ed-4a6d-b237-ecd76d719c9e
Testerman, Donna M.
5d6fe188-b3e7-45cd-b332-5c8ae7093c63

Burness, Timothy C., Ghandour, Soumaia, Marion, Claude and Testerman, Donna M. (2012) Irreducible almost simple subgroups of classical algebraic groups. Pre-print, 1-84.

Record type: Article

Abstract

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

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Submitted date: 2012
e-pub ahead of print date: 2012
Organisations: Pure Mathematics

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Local EPrints ID: 340295
URI: https://eprints.soton.ac.uk/id/eprint/340295
PURE UUID: 48403ba6-a3e3-443f-9bcb-0fe5b0b97fe6

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Date deposited: 18 Jun 2012 10:16
Last modified: 18 Jul 2017 05:46

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Contributors

Author: Timothy C. Burness
Author: Soumaia Ghandour
Author: Claude Marion
Author: Donna M. Testerman

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