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arXiv · 1611.10089

Lakshmibai-Seshadri paths and non-symmetric Cauchy identity

Seung-Il Choi·Jae-Hoon Kwon
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Abstract

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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Seung-Il Choi, Jae-Hoon Kwon. 2016-11-30. Lakshmibai-Seshadri paths and non-symmetric Cauchy identity. https://arxiv.org/abs/1611.10089

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