Invariant generalized complex geometry on maximal flag manifolds and their moduli

TL;DR

This paper explores the structure and classification of invariant generalized complex and Kähler structures on maximal flag manifolds, using pure spinors and Weyl group actions to describe their moduli spaces.

Contribution

It provides an alternative description of the moduli space of generalized complex structures via pure spinors and details a cell decomposition induced by the Weyl group.

Findings

Moduli spaces of invariant generalized complex structures are described using pure spinors.

A cell decomposition of these moduli spaces is established based on Weyl group action.

The paper characterizes invariant generalized Kähler structures on maximal flag manifolds.

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.