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Algebras and Representation Theory

, Volume 21, Issue 6, pp 1381–1394 | Cite as

Lakshmibai-Seshadri Paths and Non-Symmetric Cauchy Identity

  • Seung-Il Choi
  • Jae-Hoon Kwon
Article
  • 27 Downloads

Abstract

We give a simple crystal theoretic interpretation of the Lascoux’s expansion of a non-symmetric Cauchy kernel \({\prod }_{i+ j \leq n + 1}(1-x_{i}y_{j})^{-1}\), 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.

Keywords

Quantum groups Crystals Demazure modules 

Mathematics Subject Classification (2010)

17B37 22E46 05E10 

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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSeoul National UniversitySeoulKorea

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