Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of cluster structures in Schubert varieties   We give an explicit combinatorial description of cluster structures in
Schubert varieties of the Grassmannian in terms of (target labelings of)
Postnikov's plabic graphs. This description is a natural generalization of the
description given by (Scott 2006) for the Grassmannian and has been believed by
experts essentially since (Scott 2006), though the statement was not formally
written down until (M\"uller-Speyer 2016). To prove this conjecture we use a
result of (Leclerc 2016), who used the module category of the preprojective
algebra to prove that coordinate rings of many Richardson varieties in the
complete flag variety admit cluster structures. We also adapt a construction of
(Karpman 2016) to build cluster seeds associated to reduced expressions.
Further, we explicitly describe cluster structures in skew Schubert varieties
using plabic graphs whose boundary vertices need not be labeled in cyclic
order.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas