Parabolic subgroups and Automorphism groups of Schubert varieties

• Main Authors: Kannan, S. Senthamarai, Saha, Pinakinath
• Format: Journal Article
• Language: English
• Published: 13-08-2019
• Subjects: Mathematics - Algebraic Geometry; Mathematics - Combinatorics; Mathematics - Group Theory
• DOI: 10.48550/arxiv.1908.04768

Comptes Rendus Mathematique, Volume 356, Issue 5, May 2018, Pages
542-549 Let $G$ be a simple algebraic group of adjoint type over the field
$\mathbb{C}$ 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 $w\in W$ such that $P$ is the connected component,
containing the identity element of the group of all algebraic automorphisms of
$X(w).$