Complete reducibility: variations on a theme of Serre
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AbstractIn this note, we unify and extend various concepts in the area of G-complete reducibility, where G is a reductive algebraic group. By results of Serre and Bate–Martin–Röhrle, the usual notion of G-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of G. We show that other variations of this notion, such as relative complete reducibility and $$\sigma $$ σ -complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.
1983 ◽
Vol 27
(3)
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pp. 361-379
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1986 ◽
Vol 38
(1)
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pp. 179-214
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1971 ◽
Vol 12
(1)
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pp. 1-14
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2019 ◽
Vol 2019
(754)
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pp. 1-15