We give an explicit description of the image of a quantum LS path, regarded as a rational path, under the action of root operators, and show that the set of quantum LS paths is stable under the action of the root operators. As a by-product, we obtain a new proof of the fact that a projected level-zero LS path is just a quantum LS path.
Cite
@article{arxiv.1308.3529,
title = {Quantum Lakshmibai-Seshadri paths and root operators},
author = {Cristian Lenart and Satoshi Naito and Daisuke Sagaki and Anne Schilling and Mark Shimozono},
journal= {arXiv preprint arXiv:1308.3529},
year = {2017}
}