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 $X_{Q}(w)$.
1
Chennai Mathematical Institute, Siruseri, Kelambakkam, India
2
Tata Inst. of Fundamental Research, Colaba, Mumbai, India
S. Senthamarai Kannan; Pinakinath Saha. Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties. Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 1025-1052. http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a6/
@article{JOLT_2022_32_4_a6,
author = {S. Senthamarai Kannan and Pinakinath Saha},
title = {Minimal {Parabolic} {Subgroups} and {Automorphism} {Groups} of {Schubert} {Varieties}},
journal = {Journal of Lie Theory},
pages = {1025--1052},
year = {2022},
volume = {32},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a6/}
}
TY - JOUR
AU - S. Senthamarai Kannan
AU - Pinakinath Saha
TI - Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties
JO - Journal of Lie Theory
PY - 2022
SP - 1025
EP - 1052
VL - 32
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a6/
ID - JOLT_2022_32_4_a6
ER -
%0 Journal Article
%A S. Senthamarai Kannan
%A Pinakinath Saha
%T Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties
%J Journal of Lie Theory
%D 2022
%P 1025-1052
%V 32
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a6/
%F JOLT_2022_32_4_a6
