Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schubert varieties and free braidedness   We give a simple necessary and sufficient condition for a Schubert variety
$X_w$ to be smooth when $w$ is a freely braided element of a simply laced Weyl
group; such elements were introduced by the authors in a previous work
(math.CO/0301104). This generalizes in one direction a result of Fan concerning
varieties indexed by short-braid avoiding elements. We also derive generating
functions for the freely braided elements that index smooth Schubert varieties.
All results are stated and proved only for the simply laced case.

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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn