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CR Orbits on the complex flag manifolds of G2
Abstract
We give an explicit description of the orbits of the split real form G2(2) on the complex flag manifolds of G2 and study their induced invariant CR structures. In particular we study their Levi forms and show that all possible cases in the simple homogeneous setting occur, namely Levi nondegeneracy, k-nondegeneracy for 2≤ k≤ 3, and holomorphic degeneracy. Moreover, following the classical approach to orbits on flag manifolds, we give equations for these homogeneous CR manifolds.
Related
- The intersection of two real flag manifolds in a complex flag manifold, and the canonical form of a compact symmetric triad
- A Dolbeault complex for the contact quantised flag manifolds of type C2 and D4
- Double flag varieties of Levi type with a finite number of orbits
- Differential calculus on quantized irreducible flag manifolds
- Rational homotopy theory of flag manifolds
BibTeX
@misc{mancini2026orbits,
title = {{CR Orbits on the complex flag manifolds of $G_2$}},
author = {Donato Mancini and Stefano Marini and Costantino Medori},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10290},
eprint = {2610.10290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10290},
}
RIS
TY - UNPB
TI - CR Orbits on the complex flag manifolds of G_2
AU - Donato Mancini
AU - Stefano Marini
AU - Costantino Medori
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10290
UR - https://arxiv.org/abs/2610.10290
AB - We give an explicit description of the orbits of the split real form G_2(2) on the complex flag manifolds of G_2 and study their induced invariant CR structures. In particular we study their Levi forms and show that all possible cases in the simple homogeneous setting occur, namely Levi nondegeneracy, k-nondegeneracy for 2≤ k≤ 3, and holomorphic degeneracy. Moreover, following the classical approach to orbits on flag manifolds, we give equations for these homogeneous CR manifolds.
ER -