Given a semisimple algebraic group G, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant G x G-compactifications possessing a unique closed orbit which arise in a projective space of the shape P(End(V)), where V is a finite dimensional rational G-module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of V. In particular, we show that Sp(2r) (with r >= 1) is the unique non-adjoint simple group which admits a simple smooth compactification.

Normality and smoothness of simple linear group compactifications

J. Gandini;
2013

Abstract

Given a semisimple algebraic group G, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant G x G-compactifications possessing a unique closed orbit which arise in a projective space of the shape P(End(V)), where V is a finite dimensional rational G-module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of V. In particular, we show that Sp(2r) (with r >= 1) is the unique non-adjoint simple group which admits a simple smooth compactification.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/714364
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