An infinitesimal characterization of the complexity of homogeneous spaces (Q1288193)

The complexity of a homogeneous space \(O\) of a connected reductive group \(G\) is the minimal codimension of the orbits of a Borel subgroup \(B \subset G\) in \(O\). The authors express this complexity in terms of the relative position of the Lie algebra of the stabilizer of a generic point of \(O\) and the \(-1\)-eigenspace of a Weil involution of \(\theta\) of the Lie algebra of \(G\). A basic tool of the proof is the doubled action of \(G\) on \(O \times O\) defined by \(\theta\). Here previous work of the first author plays a central rôle.