Parabolic subgroups and Automorphism groups of Schubert varieties

S. Senthamarai Kannan; Pinakinath Saha

doi:10.1016/j.crma.2018.04.001

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arXiv · 1908.04768

Parabolic subgroups and Automorphism groups of Schubert varieties

S. Senthamarai Kannan·Pinakinath Saha

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Abstract

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 $X(w).$

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BibTeX RIS

S. Senthamarai Kannan, Pinakinath Saha. 2019-08-13. Parabolic subgroups and Automorphism groups of Schubert varieties. https://doi.org/10.1016/j.crma.2018.04.001

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