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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 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.
| Titolo: | Normality and smoothness of simple linear group compactifications | |
| Autore/i: | J. Gandini; A. Ruzzi | |
| Autore/i Unibo: | ||
| Anno: | 2013 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-012-1136-3 | |
| 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. | |
| Data stato definitivo: | 2021-02-22T18:40:04Z | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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