Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lakshmibai-Seshadri paths and non-symmetric Cauchy identity   We give a simple crystal theoretic interpretation of the Lascoux's expansion
of a non-symmetric Cauchy kernel $\prod_{i+ j\leq n+1}(1-x_iy_j)^{-1}$, which
is given in terms of Demazure characters and atoms. We give a bijective proof
of the non-symmetric Cauchy identity using the crystal of Lakshmibai-Seshadri
paths, and extend it to the case of continuous crystals.

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The categories of this paper are: adap-org
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The categories of this paper are: stat
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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: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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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: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas