The action of a real semisimple group on a complex flag manifold. I: Orbit structure and holomorphic arc components

Complex vector fields and hypoelliptic partial differential operators

“…After considering general homogeneous CR manifolds in §6, in §7 we classify all minimal orbits of real forms G of G C -homogeneous flag manifolds (see e.g. [24,1,2]) that enjoy condition (1.21). In [1, §13], together with Prof. Medori, two of the authors gave the complete classification of the essentially pseudoconcave minimal orbits.…”

Naive boundary strata and nilpotent orbits

“…In Wolf's study [27] of complex flag manifolds, it is shown thatĎ contains a unique closed orbit O c (of real codimension c c ); this is in the closure of all the other G(R)…”

“…compact imaginary, real, complex] root. (27) A character χ ∈ X * (H(C)) is depicted by shading half of the root diagram, which is meant to heuristically indicate χ −1 (R 0 ) ⊂ Λ ⊗ R. We begin with (H 0 , χ 0 ), apply a Cayley transform to get (H 1 , χ 1 ), then apply W C to both, and finally, group the results in W…”

“…This parametrizes Hodge structures on V with Hodge numbers (3,3), and a nontrivial involution (with eigenspaces V + , V + ). Alternatively, one can consider Carayol's nonclassical domain D parametrizing point-line (27) We represent the Cartan subalgebra in our root diagram by two bullets at the origin. cl(B)), or equivalently HS-with-involution on V with numbers (1, 2, 2, 1).…”

“…• -orbits are objects of some importance [11,27]. Recent work of Robles [24] has finally settled the question of maximal dimensions of integral manifolds of the infinitesimal period relation onĎ (and hence of images of period maps in Γ D).…”