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1. CMB 2012 (vol 57 pp. 97)
Rationality and the Jordan-Gatti-Viniberghi decomposition 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 Categories:20G15, 14L24 |
2. CMB 2012 (vol 57 pp. 303)
Octonion Algebras over Rings are not Determined by their Norms Answering a question of H. Petersson, we provide
a class of examples of pair of octonion algebras over a ring having isometric
norms.
Keywords:octonion algebras, torsors, descent Categories:14L24, 20G41 |
3. CMB 2003 (vol 46 pp. 204)
Rationality and Orbit Closures 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.
Categories:14L24, 20G15 |
4. CMB 2002 (vol 45 pp. 686)
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
6-dimensional irreducible module of the symmetric group $S_5$. This
module splits with respect to the icosahedral group $A_5$ into the two
standard 3-dimensional representations. The resulting linear
projections of $Q$ relate the action of $A_5$ on $Q$ to those on the
regular icosahedron.
Categories:14L24, 20B25 |