Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert series for twisted commutative algebras   Suppose that for each n >= 0 we have a representation $M_n$ of the symmetric
group S_n. Such sequences arise in a wide variety of contexts, and often
exhibit uniformity in some way. We prove a number of general results along
these lines in this paper: our prototypical theorem states that if $M_n$ can be
given a suitable module structure over a twisted commutative algebra then the
sequence $M_n$ follows a predictable pattern. We phrase these results precisely
in the language of Hilbert series (or Poincar\'e series, or formal characters)
of modules over tca's.

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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: physics