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.
Titolo: | Normality and smoothness of simple linear group compactifications | |
Autori: | ||
Data di pubblicazione: | 2013 | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-012-1136-3 | |
Parole Chiave: | Group compactifications; Semisimple algebraic groups | |
Handle: | http://hdl.handle.net/11384/10642 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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