Geodesic
The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2
Journal of Lie theory, Tome 32 (2022) no. 1, pp. 87-12
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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 
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     author = {M. Carmassi},
     title = {The {B-Orbits} on a {Hermitian} {Symmetric} {Variety} in {Characteristic} 2},
     journal = {Journal of Lie theory},
     pages = {87--12},
     year = {2022},
     volume = {32},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2022_32_1_JLT_2022_32_1_a4/}
}
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M. Carmassi. The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2. Journal of Lie theory, Tome 32 (2022) no. 1, pp. 87-12. http://geodesic.mathdoc.fr/item/JLT_2022_32_1_JLT_2022_32_1_a4/