The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2
Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 87-120
Voir la notice de l'article provenant de la source Heldermann Verlag
Let $G$ be a reductive linear algebraic group over an algebraically closed field $\mathbb{K}$ of characteristic $2$. Fix a parabolic subgroup $P$ such that the corresponding parabolic subgroup over $\mathbb{C}$ has abelian unipotent radical and fix a Levi subgroup $L\subseteq P$. We parametrize the orbits of a Borel $B\subseteq P$ over the Hermitian symmetric variety $G/L$ supposing the root system $\Phi$ is irreducible. For $\Phi$ simply laced we prove a combinatorial characterization of the Bruhat order over these orbits. We also prove a formula to compute the dimension of the orbits from combinatorial characteristics of their representatives.
Classification :
14M15
Mots-clés : Flag variety, Bruhat order, dimension formula
Mots-clés : Flag variety, Bruhat order, dimension formula
Affiliations des auteurs :
Michele Carmassi 1
Michele Carmassi. The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2. Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 87-120. http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a4/
@article{JOLT_2022_32_1_a4,
author = {Michele Carmassi},
title = {The {B-Orbits} on a {Hermitian} {Symmetric} {Variety} in {Characteristic} 2},
journal = {Journal of Lie Theory},
pages = {87--120},
year = {2022},
volume = {32},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a4/}
}