Comptes Rendus
no. 5
Algebraic geometry
Parabolic subgroups and automorphism groups of Schubert varieties

Presented by: Claire Voisin

Subramaniam Senthamarai Kannan1; Pinakinath Saha1
1 Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India
Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 542-549.

Let G be a simple algebraic group of adjoint type over the field C 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 X(w) be the Schubert variety in G/B corresponding to w. In this article we show that given any parabolic subgroup P of G containing B properly, there is an element w∈W such that P is the connected component, containing the identity element of the group of all algebraic automorphisms of X(w).

Soit G un groupe algébrique du type adjoint sur le corps des nombres complexes C et B un sous-groupe de Borel de G contenant un tore maximal T. Soit w un élément du groupe de Weil W et X(w) la variété de Schubert dans G/B 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 X(w).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2018.04.001

Subramaniam Senthamarai Kannan 1; Pinakinath Saha 1

1 Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Siruseri, Kelambakkam, 603103, India 
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Subramaniam Senthamarai Kannan; Pinakinath Saha. Parabolic subgroups and automorphism groups of Schubert varieties. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 542-549. doi : 10.1016/j.crma.2018.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.001/

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