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arXiv · 2610.10290

CR Orbits on the complex flag manifolds of $G_2$

Donato Mancini·Stefano Marini·Costantino Medori
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Abstract

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 $2\leq k\leq 3$, and holomorphic degeneracy. Moreover, following the classical approach to orbits on flag manifolds, we give equations for these homogeneous CR manifolds.

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Donato Mancini, Stefano Marini, Costantino Medori. 2026-10-07. CR Orbits on the complex flag manifolds of $G_2$. https://arxiv.org/abs/2610.10290

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