Journal of Lie Theory

no. 1
The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 87-120
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.
DOI: 10.5802/jolt.1221
Classification: 14M15
Keywords: Flag variety, Bruhat order, dimension formula 
@article{JOLT_2022_32_1_a4,
     author = {M. 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},
     doi = {10.5802/jolt.1221},
     zbl = {1492.14088},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1221/}
}
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M. Carmassi. The B-Orbits on a Hermitian Symmetric Variety in Characteristic 2. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 87-120. doi: 10.5802/jolt.1221

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