Journal of Lie Theory

no. 4
Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1025-1052
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 $X_{Q}(w)$.
DOI: 10.5802/jolt.1264
Classification: 14M15, 14M17
Keywords: Minuscule weights, co-minuscule roots, Schubert varieties, automorphism groups 
@article{JOLT_2022_32_4_a6,
     author = {S. S. Kannan and P. 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},
     doi = {10.5802/jolt.1264},
     zbl = {1508.14057},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1264/}
}
TY  - JOUR
AU  - S. S. Kannan
AU  - P. 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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1264/
DO  - 10.5802/jolt.1264
ID  - JOLT_2022_32_4_a6
ER  - 
%0 Journal Article
%A S. S. Kannan
%A P. 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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.1264/
%R 10.5802/jolt.1264
%F JOLT_2022_32_4_a6
S. S. Kannan; P. Saha. Minimal Parabolic Subgroups and Automorphism Groups of Schubert Varieties. Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 1025-1052. doi: 10.5802/jolt.1264

Cited by Sources: