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Displaying similar documents to “On the complicatedness of the pair (g,K).”

Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser (1995)

Annales de l'institut Fourier

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Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular ℤ -cohomology of a point. Suppose that G is a complex algebraic group acting algebraically on X . Our main results are the following: if G is semi-simple, then the generic fiber of the quotient map π : X → X / / G contains a dense orbit. If G is connected and reductive, then the action has fixed points if dim X / / G ≤ 3 .

An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras

Dmitri I. Panyushev (2005)

Annales de l’institut Fourier

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We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation...