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Search: MSC category 14L24 ( Geometric invariant theory [See also 13A50] )

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1. CMB 2012 (vol 57 pp. 97)

Levy, Jason
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)

Gille, Philippe
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)

Levy, Jason
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)

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 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

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