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Journal of Lie Theory 16 (2006), No. 1, 039--046
Copyright Heldermann Verlag 2006

On Exceptional Completions of Symmetric Varieties

Rocco Chirivý
Dip. di Matematica, UniversitÓ di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

Andrea Maffei
Dip. di Matematica, UniversitÓ di Roma "La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy


Let $G$ be a simple group with an exceptional involution $\sigma$ having $H$ as fixed point set. We study the embedding of $G/H$ in the projective space ${\mathbb P}(V)$ for a simple $G$--module $V$ with a line fixed by $H$ but having no nonzero vector fixed by $H$. For a certain class of such modules $V$ we describe the closure of $G/H$ proving in particular that it is a smooth variety.

Keywords: Complete symmetric variety, exceptional involution.

MSC: 14M17, 14L30

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