We verify our earlier conjecture and use it to prove that the semisimple parts of the rational Jordan-Kac-Vinberg decompositions of a rational vector all lie in a single rational orbit.

Keywords:

reductive group, $G$-module, Jordan decomposition, orbit closure, rationality reductive group, $G$-module, Jordan decomposition, orbit closure, rationality

MSC Classifications:

20G15, 14L24 show english descriptions Linear algebraic groups over arbitrary fields
Geometric invariant theory [See also 13A50] 20G15 - Linear algebraic groups over arbitrary fields
14L24 - Geometric invariant theory [See also 13A50]

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