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- W2023376370 abstract "Consider a class of pairs ( g , g 1 ) , where g is a semisimple Lie algebra and g 1 is a subalgebra reductive in g , satisfying the following: For any Cartan subalgebra h 1 ⊆ g 1 there is a unique Cartan subalgebra h ⊆ g containing h 1 . Given such a pair ( g , g 1 ) and a Borel subalgebra b 1 ⊆ g 1 we study a (finite) set S Bor g ( b 1 ) of all Borel subalgebras b ⊆ g containing b 1 . In particular we point at the subclass of pairs ( g , g 1 ) when S Bor g ( b 1 ) is a singleton, for every Borel subalgebra b 1 ⊆ g 1 . As a consequence, for such pairs we relate the corresponding flag varieties B ( g ) and B ( g 1 ) . As an interesting class of pairs ( g , g 1 ) , for which we can apply our results on pairs of Borel subalgebras, we study in detail the pairs considered by R. Brylinski and B. Kostant related to shared orbit pairs." @default.
- W2023376370 created "2016-06-24" @default.
- W2023376370 creator A5003525865 @default.
- W2023376370 date "2015-02-01" @default.
- W2023376370 modified "2023-09-29" @default.
- W2023376370 title "Compatible pairs of Borel subalgebras and shared orbit pairs" @default.
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- W2023376370 doi "https://doi.org/10.1016/j.jalgebra.2014.10.035" @default.
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