LAUSR

Abstract Let G be a complex semi-simple Lie group and form its maximal flag manifold F = G ∕ P = U ∕ T where P is a minimal parabolic subgroup, U a compact real form and T = U ∩ P a maximal torus of U . The aim of this paper is to study invariant generalized complex structures on F . We describe the invariant generalized almost complex structures on F and classify which one is integrable. The problem reduces to the study of invariant 4-dimensional generalized almost complex structures restricted to each root space, and for integrability we analyze the Nijenhuis operator for a triple of roots such that its sum is zero. We also conducted a study about twisted generalized complex structures. We define a new bracket ‘twisted’ by a closed 3-form Ω and also define the Nijenhuis operator twisted by Ω . We classify the Ω -integrable generalized complex structure.