Alcove walks, crystal structure and a Levi branching rule

Wenzhuo Wang

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arXiv · 2610.41929

Alcove walks, crystal structure and a Levi branching rule

Wenzhuo Wang

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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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Wenzhuo Wang. 2026-10-30. Alcove walks, crystal structure and a Levi branching rule. https://arxiv.org/abs/2610.41929

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