Geodesic
Rationality and Orbit Closures
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 204-215

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DOI

Suppose we are given a finite-dimensional vector space $V$ equipped with an $F$ -rational action of a linearly algebraic group $G$ , with $F$ a characteristic zero field. We conjecture the following: to each vector $v\,\in \,V(F)$ there corresponds a canonical $G(F)$ -orbit of semisimple vectors of $V$ . In the case of the adjoint action, this orbit is the $G(F)$ -orbit of the semisimple part of $v$ , so this conjecture can be considered a generalization of the Jordan decomposition. We prove some cases of the conjecture.
DOI : 10.4153/CMB-2003-021-6
Mots-clés : 14L24, 20G15 
Levy, Jason. Rationality and Orbit Closures. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 204-215. doi: 10.4153/CMB-2003-021-6
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