Irreducible Subgroups of Exceptional Algebraic Groups

Donna M. Testerman

Jan 1988 · American Mathematical Society: Memoirs of the American Mathematical Society Ibhuku elingu-390 · American Mathematical Soc.

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Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.