TL;DR
This paper constructs a compatible action of the cactus group on a Weyl group W, using wall-crossing bijections related to Kazhdan-Lusztig cells, linking combinatorics with category O functors.
Contribution
It introduces a new action of the cactus group on W that aligns with Kazhdan-Lusztig cell structures, bridging combinatorics and representation theory.
Findings
Defined a cactus group action on W compatible with cells
Connected wall-crossing bijections to functors in category O
Provided combinatorial models for wall-crossing phenomena
Abstract
The goal of this paper is to construct an action of the cactus group of a Weyl group W on W that is nicely compatible with Kazhdan-Lusztig cells. The action is realized by the wall-crossing bijections that are combinatorial shadows of wall-crossing functors on the category O.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models