Rationality and the Jordan–Gatti–Viniberghi Decomposition
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 97-104

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2012-039-0
Mots-clés : 20G15, 14L24, reductive group, G-module, Jordan decomposition, orbit closure, rationality
Levy, Jason. Rationality and the Jordan–Gatti–Viniberghi Decomposition. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 97-104. doi: 10.4153/CMB-2012-039-0
@article{10_4153_CMB_2012_039_0,
     author = {Levy, Jason},
     title = {Rationality and the {Jordan{\textendash}Gatti{\textendash}Viniberghi} {Decomposition}},
     journal = {Canadian mathematical bulletin},
     pages = {97--104},
     year = {2014},
     volume = {57},
     number = {1},
     doi = {10.4153/CMB-2012-039-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-039-0/}
}
TY  - JOUR
AU  - Levy, Jason
TI  - Rationality and the Jordan–Gatti–Viniberghi Decomposition
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 97
EP  - 104
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-039-0/
DO  - 10.4153/CMB-2012-039-0
ID  - 10_4153_CMB_2012_039_0
ER  - 
%0 Journal Article
%A Levy, Jason
%T Rationality and the Jordan–Gatti–Viniberghi Decomposition
%J Canadian mathematical bulletin
%D 2014
%P 97-104
%V 57
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-039-0/
%R 10.4153/CMB-2012-039-0
%F 10_4153_CMB_2012_039_0

[1] [1] Bardsley, Peter and Richardson, R.W., Ètale slices for algebraic transformation groups incharacteristic p. Proc. London Math. Soc. 51 (1985), 295–317, 1985. Google Scholar | DOI

[2] [2] Bate, M., Martin, B., Röhrle, G., and Tange, R., Closed Orbits and uniform S-instability in GeometricInvariant Theory. Trans. Amer. Math. Soc., to appear. arxiv:0904.4853v4. Google Scholar

[3] [3] Borel, Armand, Linear algebraic groups. Second edition. Graduate Texts in Math. 126, Springer-Verlag, New York, 1991. Google Scholar

[4] [4] Borel, Armand and Tits, Jacques, Groupes réductifs. Inst. Hautes E´ tudes Sci. Publ. Math. 27 (1965), 55–150. Google Scholar

[5] [5] Bremigan, Ralph J., Quotients for algebraic group actions over non-algebraically closed fields. J. Reine Angew. Math. 453 (1994), 21–47. Google Scholar

[6] [6] Gatti, V. and Viniberghi, E., Spinors of 13-dimensional space. Adv. in Math. 30 (1978), 137–155. Google Scholar | DOI

[7] [7] Kac, V. G., Infinite root systems, representations of graphs and invariant theory. II. J. Algebra 78 (1982), 141–162. Google Scholar | DOI

[8] [8] Kempf, George R., Instability in invariant theory. Ann. of Math. (2) 108 (1978), 299–316. Google Scholar | DOI

[9] [9] Levy, Jason, A truncated Poisson formula for groups of rank at most two. Amer. J. Math. 117 (1995), 1371–1408. Google Scholar | DOI

[10] [10] Levy, Jason, Rationality and orbit closures. Canad. Math. Bull. 46 (2003), 204–215. Google Scholar | DOI

[11] [11] Richardson, R.W., Conjugacy classes of n-tuples in Lie algebras and algebraic groups. Duke Math. J. 57 (1988), 1–35. Google Scholar | DOI

Cité par Sources :