1. CMB 2012 (vol 57 pp. 97)
 Levy, Jason

Rationality and the JordanGattiViniberghi decomposition
We verify
our earlier conjecture
and use it to prove that the
semisimple parts of the rational JordanKacVinberg decompositions of
a rational vector all lie in a single rational orbit.
Keywords:reductive group, $G$module, Jordan decomposition, orbit closure, rationality Categories:20G15, 14L24 

2. CMB 2012 (vol 57 pp. 303)
3. CMB 2003 (vol 46 pp. 204)
 Levy, Jason

Rationality and Orbit Closures
Suppose we are given a finitedimensional 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.
Categories:14L24, 20G15 

4. CMB 2002 (vol 45 pp. 686)
 Rauschning, Jan; Slodowy, Peter

An Aspect of Icosahedral Symmetry
We embed the moduli space $Q$ of 5 points on the projective line
$S_5$equivariantly into $\mathbb{P} (V)$, where $V$ is the
6dimensional irreducible module of the symmetric group $S_5$. This
module splits with respect to the icosahedral group $A_5$ into the two
standard 3dimensional representations. The resulting linear
projections of $Q$ relate the action of $A_5$ on $Q$ to those on the
regular icosahedron.
Categories:14L24, 20B25 
