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Alcove walks, crystal structure and a Levi branching rule
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 a
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