Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke
  Algebra of the Symmetric Group   Building on the work of P.N. Norton, we give combinatorial formulae for two
maximal decompositions of the identity into orthogonal idempotents in the
$0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This
construction is compatible with the branching from $S_{N-1}$ to $S_{N}$.

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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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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: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph