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Commutative Subalgebras and Sphericity in Z2-Graded Lie Algebras

Authors:	Panyushev Dmitri I

Institution:	Independent University of Moscow Bol'shoi Vlasevskii per. 11, 119002 Moscow, Russia

Abstract:	Let g = g₀ ${oplus}$ g₁ be a Z₂-graded simple Lie algebra. Fix a Borelsubalgebra b₀ $sub$ g₀. Let a $sub$ g₁ be a b₀-stable subalgebra. Then a isautomatically commutative. It is known that if is a spherical G-variety, then G₀.a is a sphericalG₀-variety. We describe all Z₂-gradings having the propertythat is a spherical G-varietyfor any a. 2000 Mathematics Subject Classification 14L30, 17B20,20E46.

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