Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Details Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

2000-12-20

arxiv.org/abs/math/0012206v2

Mathematics

Representation Theory

24 pages, corrected variant

Scientific paper

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.

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