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Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras

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JournalMathematische Zeitschrift
DatePublished - Dec 2011
Issue number3-4
Volume269
Number of pages24
Pages (from-to)809-832
Original languageEnglish

Abstract

Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on Gn, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic characterization of the closed H-orbits in Gn, generalizing work of Richardson which treats the case H = G. This characterization turns out to be a natural generalization of Serre’s notion of Gcomplete reducibility. This concept appears to be new, even in characteristic zero. We discuss how to extend some key results on G-complete reducibility in this framework. We also consider some rationality questions.

    Research areas

  • Algebra

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