Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Beilinson-Drinfeld Grassmannian and symplectic knot homology   Seidel-Smith and Manolescu constructed knot homology theories using
symplectic fibrations whose total spaces were certain varieties of matrices.
These knot homology theories were associated to $SL(n) $ and tensor products of
the standard and dual representations. In this paper, we place their geometric
setups in a natural, general framework. For any complex reductive group and any
sequence of minuscule dominant weights, we construct a fibration of affine
varieties over a configuration space. The middle cohomology of these varieties
is isomorphic to the space of invariants in the corresponding tensor product of
representations. Our construction uses the Beilinson-Drinfeld Grassmannian and
the geometric Satake correspondence.

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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex