Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Lie Theory 32 (2022), No. 4, 1025--1052
Copyright Heldermann Verlag 2022

Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties

S. Senthamarai Kannan
Chennai Mathematical Institute, Siruseri, Kelambakkam, India

Pinakinath Saha
Tata Inst. of Fundamental Research, Colaba, Mumbai, India


Let $G$ be a simple simply-laced 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, co-minuscule roots, Schubert varieties, automorphism groups.

MSC: 14M15, 14M17.

[ Fulltext-pdf  (206  KB)] for subscribers only.