Minimal Parabolic subgroups and Automorphism groups of Schubert varieties-II

S. Senthamarai Kannan; Pinakinath Saha

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arXiv · 2209.12838

Minimal Parabolic subgroups and Automorphism groups of Schubert varieties-II

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 $G.$ In this article, we show that $\alpha$ is a co-minuscule root if and only if for any parabolic subgroup $Q$ containing $B$ properly, there is no Schubert variety $X_{Q}(w)$ in $G/Q$ such that the minimal parabolic subgroup $P_{\alpha}$ of $G$ is the connected component, containing the identity automorphism of the group of all algebraic automorphisms of $X_{Q}(w).$

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BibTeX RIS

S. Senthamarai Kannan, Pinakinath Saha. 2022-09-26. Minimal Parabolic subgroups and Automorphism groups of Schubert varieties-II. https://arxiv.org/abs/2209.12838

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