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Compatible pairs of Borel subalgebras and shared orbit pairs (CROSBI ID 214063)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Širola, Boris Compatible pairs of Borel subalgebras and shared orbit pairs // Journal of algebra, 423 (2015), 726-766. doi: 10.1016/j.jalgebra.2014.10.035

Podaci o odgovornosti

Širola, Boris

engleski

Compatible pairs of Borel subalgebras and shared orbit pairs

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 in g_1 there is a unique Cartan subalgebra h in g containing h_1. Given such a pair (g, g_1) and a Borel subalgebra b_1 in g_1 we study a (finite) set S_{; ; ; Bor}; ; ; ^g(b_1) of all Borel subalgebras b in 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 in 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.

semisimple Lie algebra; Cartan subalgebra; root; root system; Borel subalgebra; pair of Lie algebras; shared orbit pair; nilpotent element; nilpotent orbit

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Podaci o izdanju

423

2015.

726-766

objavljeno

0021-8693

10.1016/j.jalgebra.2014.10.035

Povezanost rada

Matematika

Poveznice
Indeksiranost