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Rationality and Orbit Closures

  Published:2003-06-01
 Printed: Jun 2003
  • Jason Levy
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Abstract

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

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