Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant Generalized Complex Structures on Flag Manifolds   Let $G$ be a complex semi-simple Lie group and form its maximal flag manifold
$\mathbb{F}=G/P=U/T$ where $P$ is a minimal parabolic subgroup, $U$ a compact
real form and $T=U\cap P$ a maximal torus of $U$. The aim of this paper is to
study invariant generalized complex structures on $\mathbb{F}$. We describe the
invariant generalized almost complex structures on $\mathbb{F}$ 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 analyse 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 $\Omega $ and also define the Nijenhuis operator twisted by $\Omega $.
We classify the $\Omega $-integrable generalized complex structure.

5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga