Invariant generalized complex geometry on maximal flag manifolds and their moduli

Abstract: We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized K\"ahler structures on maximal flag manifolds under $B$-transformations. We give an alternative description of the moduli space of generalized complex structures using pure spinors, and describe a cell decomposition of these moduli spaces induced by the action of the Weyl group.