Normality and non-normality of group compactifications in simple projective spaces
[Normalité et non-normalité des plongements d’un groupe dans un espace projectif simple]
Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2435-2461.

Étant donné une représentation irreductible V d’un groupe complexe semi-simple et simplement connexe G, nous considérons l’adhérence X de l’image de G dans (End(V)). Nous déterminons les représentations V pour lesquelles X est normale, respectivement lisse.

Given an irreducible representation V of a complex simply connected semisimple algebraic group G we consider the closure X of the image of G in (End(V)). We determine for which V the variety X is normal and for which V is smooth.

DOI : 10.5802/aif.2679
Classification : 14L30, 14M17
Keywords: semisimple algebraic groups, group compactifications
Mot clés : groupes algébriques semi-simples, plongements projectifs d’un groupe
Bravi, Paolo 1 ; Gandini, Jacopo 1 ; Maffei, Andrea 1 ; Ruzzi, Alessandro 1

1 Dip.to di Matematica Università di Roma “La Sapienza” P.le A. Moro, 5 00185 ROMA ITALY
@article{AIF_2011__61_6_2435_0,
     author = {Bravi, Paolo and Gandini, Jacopo and Maffei, Andrea and Ruzzi, Alessandro},
     title = {Normality and non-normality of group compactifications in simple projective spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {2435--2461},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     doi = {10.5802/aif.2679},
     mrnumber = {2976317},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2679/}
}
TY  - JOUR
AU  - Bravi, Paolo
AU  - Gandini, Jacopo
AU  - Maffei, Andrea
AU  - Ruzzi, Alessandro
TI  - Normality and non-normality of group compactifications in simple projective spaces
JO  - Annales de l'Institut Fourier
PY  - 2011
SP  - 2435
EP  - 2461
VL  - 61
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.2679/
DO  - 10.5802/aif.2679
LA  - en
ID  - AIF_2011__61_6_2435_0
ER  - 
%0 Journal Article
%A Bravi, Paolo
%A Gandini, Jacopo
%A Maffei, Andrea
%A Ruzzi, Alessandro
%T Normality and non-normality of group compactifications in simple projective spaces
%J Annales de l'Institut Fourier
%D 2011
%P 2435-2461
%V 61
%N 6
%I Association des Annales de l’institut Fourier
%U http://www.numdam.org/articles/10.5802/aif.2679/
%R 10.5802/aif.2679
%G en
%F AIF_2011__61_6_2435_0
Bravi, Paolo; Gandini, Jacopo; Maffei, Andrea; Ruzzi, Alessandro. Normality and non-normality of group compactifications in simple projective spaces. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2435-2461. doi : 10.5802/aif.2679. http://www.numdam.org/articles/10.5802/aif.2679/

[1] Bourbaki, N. Éléments de mathématique, Fasc. XXXIV. Groupes et algèbres de Lie. Chapitres IV, V, VI, Actualités Scientifiques et Industrielles, 1337, Hermann Paris, 1968 | MR | Zbl

[2] Brion, M. Variétés sphériques et théorie de Mori, Duke Math. J., Volume 72 (1993) no. 2, pp. 369-404 | DOI | MR | Zbl

[3] Chirivì, R.; De Concini, C.; Maffei, A. On normality of cones over symmetric varieties, Tohoku Math. J. (2), Volume 58 (2006) no. 4, pp. 599-616 | DOI | MR | Zbl

[4] Chirivì, R.; Maffei, A. Projective normality of complete symmetric varieties, Duke Math. J., Volume 122 (2004), pp. 93-123 | DOI | MR | Zbl

[5] De Concini, C. Normality and non normality of certain semigroups and orbit closures, Algebraic transformation groups and algebraic varieties (Encyclopaedia Math. Sci.), Volume 132, Springer, Berlin, 2004, pp. 15-35 | MR | Zbl

[6] De Concini, C.; Procesi, C. Complete symmetric varieties, Invariant Theory (Lecture Notes in Math.), Volume 996, Springer, Berlin, 1983, pp. 1-44 | Zbl

[7] Kannan, S.S. Projective normality of the wonderful compactification of semisimple adjoint groups, Math. Z., Volume 239 (2002), pp. 673-682 | DOI | MR | Zbl

[8] Knop, F. The Luna-Vust theory of spherical embeddings, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), Manoj Prakashan, Madras (1991), pp. 225-249 | MR | Zbl

[9] Knop, F.; Kraft, H.; Luna, D.; Vust, T. Local properties of algebraic group actions, DMV Sem., Volume 13 (1989), pp. 63-75 | MR | Zbl

[10] Ruzzi, A. Smooth projective symmetric varieties with Picard number equal to one (To appear in Internat. J. Math)

[11] Stembridge, J.R. The partial order of dominant weights, Adv. Math., Volume 136 (1998) no. 2, pp. 340-364 | DOI | MR | Zbl

[12] Timashev, D.A. Equivariant compactifications of reductive groups, Sb. Math., Volume 194 (2003) no. 3-4, pp. 589-616 | DOI | MR | Zbl

[13] Vust, Th. Plongements d’espaces symétriques algébriques: une classification, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), Volume 17 (1990) no. 2, pp. 165-195 | Numdam | MR | Zbl

Cité par Sources :