[Sous-groupes paraboliques et groupes d'automorphismes des variétés de Schubert]
Soit G un groupe algébrique du type adjoint sur le corps des nombres complexes et B un sous-groupe de Borel de G contenant un tore maximal T. Soit w un élément du groupe de Weil W et la variété de Schubert dans correspondant à w. Dans cet article, nous montrons que, pour tout sous-groupe parabolique P de G contenant B, il existe un élément w dans W tel que P est la composante connexe contenant l'élément identité du groupe des automorphismes algébriques de .
Let G be a simple algebraic group of adjoint type over the field of complex numbers, B be a Borel subgroup of G containing a maximal torus T of G. Let w be an element of the Weyl group W and be the Schubert variety in corresponding to w. In this article we show that given any parabolic subgroup P of G containing B properly, there is an element such that P is the connected component, containing the identity element of the group of all algebraic automorphisms of .
Accepté le :
Publié le :
@article{CRMATH_2018__356_5_542_0,
author = {Kannan, Subramaniam Senthamarai and Saha, Pinakinath},
title = {Parabolic subgroups and automorphism groups of {Schubert} varieties},
journal = {Comptes Rendus. Math\'ematique},
pages = {542--549},
publisher = {Elsevier},
volume = {356},
number = {5},
year = {2018},
doi = {10.1016/j.crma.2018.04.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.04.001/}
}
TY - JOUR AU - Kannan, Subramaniam Senthamarai AU - Saha, Pinakinath TI - Parabolic subgroups and automorphism groups of Schubert varieties JO - Comptes Rendus. Mathématique PY - 2018 SP - 542 EP - 549 VL - 356 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.04.001/ DO - 10.1016/j.crma.2018.04.001 LA - en ID - CRMATH_2018__356_5_542_0 ER -
%0 Journal Article %A Kannan, Subramaniam Senthamarai %A Saha, Pinakinath %T Parabolic subgroups and automorphism groups of Schubert varieties %J Comptes Rendus. Mathématique %D 2018 %P 542-549 %V 356 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.04.001/ %R 10.1016/j.crma.2018.04.001 %G en %F CRMATH_2018__356_5_542_0
Kannan, Subramaniam Senthamarai; Saha, Pinakinath. Parabolic subgroups and automorphism groups of Schubert varieties. Comptes Rendus. Mathématique, Tome 356 (2018) no. 5, pp. 542-549. doi : 10.1016/j.crma.2018.04.001. http://www.numdam.org/articles/10.1016/j.crma.2018.04.001/
[1] Lie Group Actions in Complex Analysis, Aspects of Mathematics, vol. E 27, Vieweg, Braunschweig/Wiesbaden, Germany, 1995
[2] Cohomology of line bundles on Schubert varieties—I, Transform. Groups, Volume 9 (2004) no. 2, pp. 105-131
[3] Lie Groups and Lie Algebras, Chapters 4–6, Springer-Verlag, Berlin, Heidelberg, New York, 2002
[4] On automorphism groups of fiber bundles, Publ. Mat. Urug., Volume 12 (2011), pp. 39-66
[5] Frobenius Splitting Methods in Geometry and Representation Theory, Progress in Mathematics, vol. 231, Birkhäuser, Boston, Inc., Boston, MA, USA, 2005
[6] A very simple proof of Bott's theorem, Invent. Math., Volume 33 (1976), pp. 271-272
[7] Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1972
[8] Linear Algebraic Groups, Springer-Verlag, Berlin, Heidelberg, New York, 1975
[9] Representations of Algebraic Groups, Mathematical Surveys and Monographs, vol. 107, 2003
[10] On the automorphism group of a smooth Schubert variety, Algebr. Represent. Theory, Volume 19 (2016) no. 4, pp. 761-782
[11] Criterion for smoothness of Schubert varieties in , Proc. Indian Acad. Sci. Math. Sci., Volume 100 (1990) no. 1, pp. 45-52
[12] Representability of group functors, and automorphisms of algebraic schemes, Invent. Math., Volume 4 (1967), pp. 1-25
Cité par Sources :
