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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
chirivi@dm.unipi.it

Andrea Maffei
Dip. di Matematica, UniversitÓ di Roma "La Sapienza", P.le Aldo Moro 5, 00185 Roma, Italy
amaffei@mat.uniroma1.it



[Abstract-pdf]

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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