Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine nil-Hecke algebras and braided differential structure on affine
  Weyl groups   We construct a model of the affine nil-Hecke algebra as a subalgebra of the
Nichols-Woronowicz algebra associated to a Yetter-Drinfeld module over the
affine Weyl group. We also discuss the Peterson isomorphism between the
homology of the affine Grassmannian and the small quantum cohomology ring of
the flag variety in terms of the braided differential calculus.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an