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EnglishGiven a semisimple algebraic group G, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant G×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.
| Titolo: | Normality and smoothness of simple linear group compactifications |
| Autori: | |
| Data di pubblicazione: | 2013 |
| Rivista: | |
| Abstract: | Given a semisimple algebraic group G, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant G×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. |
| Handle: | http://hdl.handle.net/11384/10642 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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