Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian fibers of Gelfand-Cetlin systems   A Gelfand-Cetlin system is a completely integrable system defined on a
partial flag manifold whose image is a rational convex polytope called a
Gelfand-Cetlin polytope. Motivated by the study of Nishinou-Nohara-Ueda on the
Floer theory of Gelfand-Cetlin systems, we provide a detailed description of
topology of Gelfand-Cetlin fibers. In particular, we prove that any fiber over
an interior point of a k-dimensional face of the Gelfand-Cetlin polytope is an
isotropic submanifold and is diffeomorphic to $(S^1)^k \times N$ for some
smooth manifold $N$. We also prove that such $N$'s are exactly the vanishing
cycles shrinking to points in the associated toric variety via the toric
degeneration. We also devise an algorithm of reading off Lagrangian fibers from
the combinatorics of the ladder diagram.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs