Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On enumeration in classical invariant theory   In this paper we study the Frobenius characters of the invariant subspaces of
the tensor powers of a representation V. The main result is a formula for these
characters for a polynomial functor of V involving the characters for V. The
main application is to representations V for which these characters are known.
The best understood case is for V the vector representation of a symplectic
group or special linear group. Other cases where there are some related results
are the defining representations of the symmetric groups and the adjoint
representations of the general linear groups. This formula uses methods of
enumerative combinatorics and in particular is similar to the cycle index
series of regular graphs.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs