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Alcove walks, crystal structure and a Levi branching rule
Abstract
In the Borel case P=B, we endow Haines' set of maximal-dimensional positively folded alcove walks (arXiv:2405.17174) with a crystal structure. We construct a bijection with the LS-gallery model of Gaussent and Littelmann (arXiv:math/0307122) and prove that it intertwines the root operators. This answers a question raised by Haines. We also extend the Gaussent-Littelmann stratification to the parabolic setting, prove the Levi branching rule for LS galleries, and compare the resulting gallery model with Haines' maximal-dimensional positively folded alcove walks in the parabolic setting.
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BibTeX
@misc{wang2026alcove,
title = {{Alcove walks, crystal structure and a Levi branching rule}},
author = {Wenzhuo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41929},
eprint = {2610.41929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41929},
}
RIS
TY - UNPB
TI - Alcove walks, crystal structure and a Levi branching rule
AU - Wenzhuo Wang
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41929
UR - https://arxiv.org/abs/2610.41929
AB - In the Borel case P=B, we endow Haines' set of maximal-dimensional positively folded alcove walks (arXiv:2405.17174) with a crystal structure. We construct a bijection with the LS-gallery model of Gaussent and Littelmann (arXiv:math/0307122) and prove that it intertwines the root operators. This answers a question raised by Haines. We also extend the Gaussent-Littelmann stratification to the parabolic setting, prove the Levi branching rule for LS galleries, and compare the resulting gallery model with Haines' maximal-dimensional positively folded alcove walks in the parabolic setting.
ER -