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Publication - Dr Tim Burness

    Irreducible almost simple subgroups of classical algebraic groups

    Citation

    Burness, TC, Ghandour, S, Marion, C & Testerman, DM, 2015, ‘Irreducible almost simple subgroups of classical algebraic groups’. Memoirs of the American Mathematical Society, vol 236.

    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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