Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of symplectic invariant tensors   An important problem from invariant theory is to describe the subspace of a
tensor power of a representation invariant under the action of the group.
According to Weyl's classic, the first main (later: 'fundamental') theorem of
invariant theory states that all invariants are expressible in terms of a
finite number among them, whereas a second main theorem determines the
relations between those basic invariants.
  Here we present a transparent, combinatorial proof of a second fundamental
theorem for the defining representation of the symplectic group Sp(2n). Our
formulation is completely explicit and provides a very precise link to
(n+1)-noncrossing perfect matchings, going beyond a dimension count. As a
corollary, we obtain an instance of the cyclic sieving phenomenon.

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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom