Equivariant compactifications of reductive groups

Abstract

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under the action of the doubled group by left/right multiplications, the local structure in a neighborhood of a closed orbit, and obtain some conditions of normality and smoothness of a compactification. Our methods of research use the theory of equivariant embeddings of spherical homogeneous spaces and of reductive algebraic semigroups.

30 pages, AmSLaTeX. Bibliography: 36 items

References in corpus (3)

• Hypergeometric functions on reductive groups
• Stable reductive varieties II: Projective case
• Stable reductive varieties I: Affine varieties

Cited by in corpus (10)

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• Smooth Projective Symmetric Varieties with Picard Number equal to one
• Normality and non-normality of group compactifications in simple projective spaces
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• K-stability of Gorenstein Fano group compactifications with rank two
• Simple linear compactifications of odd orthogonal groups
• Affine embeddings of a reductive group
• Group Compactifications and Moduli Spaces
• The cone of semisimple monoids with the same factorial hull
• Geometrical description of smooth projective symmetric varieties with Picard number one