
Journal of Lie Theory 32 (2022), No. 4, 10251052 Copyright Heldermann Verlag 2022 Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties S. Senthamarai Kannan Chennai Mathematical Institute, Siruseri, Kelambakkam, India kannan@cmi.ac.in Pinakinath Saha Tata Inst. of Fundamental Research, Colaba, Mumbai, India psaha@math.tifr.res.in [Abstractpdf] Let $G$ be a simple simplylaced 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 $\omega_\alpha$ is a minuscule fundamental weight 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 $X_{Q}(w)$. Keywords: Minuscule weights, cominuscule roots, Schubert varieties, automorphism groups. MSC: 14M15, 14M17. [ Fulltextpdf (206 KB)] for subscribers only. 