Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isotropic submanifolds and coadjoint orbits of the Hamiltonian group   We describe a class of coadjoint orbits of the group of Hamiltonian
diffeomorphisms of a symplectic manifold $(M,\omega)$ by implementing
symplectic reduction for the dual pair associated to the Hamiltonian
description of ideal fluids. The description is given in terms of nonlinear
Grassmannians (manifolds of submanifolds) with additional geometric structures.
Reduction at zero momentum yields the identification of coadjoint orbits with
Grassmannians of isotropic volume submanifolds, slightly generalizing the
results in Weinstein [1990] and Lee [2009]. At the other extreme, the case of a
nondegenerate momentum recovers the identification of connected components of
the nonlinear symplectic Grassmannian with coadjoint orbits, thereby recovering
the result of Haller and Vizman [2004]. We also comment on the intermediate
cases which correspond to new classes of coadjoint orbits. The description of
these coadjoint orbits as well as their orbit symplectic form is obtained in a
systematic way by exploiting the general properties of dual pairs of momentum
maps. We also show that whenever the symplectic manifold $(M,\omega)$ is
prequantizable, the coadjoint orbits that consist of isotropic submanifolds
with total volume $a\in\mathbb{Z}$ are prequantizable. The prequantum bundle is
constructed explicitly and, in the Lagrangian case, recovers the Berry bundle
constructed in Weinstein [1990].

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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg