Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A cluster structure on the coordinate ring of partial flag varieties   The main goal of this paper is to show that the (multi-homogeneous)
coordinate ring of a partial flag variety $\mathbb{C} [G / P_K^{-}]$ admits a
cluster algebra structure if $G$ is any simply-connected semisimple complex
algebraic group. We use derivation properties and a special lifting map to
prove that the cluster algebra structure $\mathcal{A}$ of the coordinate ring
$\mathbb{C}[N_K]$ of a Schubert cell constructed by Goodearl and Yakimov can be
lifted, in an explicit way, to a cluster structure $\hat{\mathcal{A}}$ living
in the coordinate ring of the corresponding partial flag variety. Then we use a
minimality condition to prove that the cluster algebra $\hat{\mathcal{A}}$ is
indeed equal to $\mathbb{C}[G / P_K^{-}]$.

4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph