Let $G$ be a simply connected semisimple algebraic group and let $K$ be the subgroup of points fixed by an involution of $G$. For certain representations containing a line $r$ preserved by $K$, we study the normality of the closure of the set of vectors which are $G$ conjugate to a vector in $r$. Some applications of our result to the normality of certain classical varieties are given.
@article{1170347692,
author = {Chiriv\`\i , Rocco and De Concini, Corrado and Maffei, Andrea},
title = {On normality of cones over symmetric varieties},
journal = {Tohoku Math. J. (2)},
volume = {58},
number = {1},
year = {2006},
pages = { 599-616},
language = {en},
url = {http://dml.mathdoc.fr/item/1170347692}
}
Chirivì, Rocco; De Concini, Corrado; Maffei, Andrea. On normality of cones over symmetric varieties. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp. 599-616. http://gdmltest.u-ga.fr/item/1170347692/