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arXiv · 2301.10457

Order types of reflection orders on affine Weyl groups

Weijia Wang·Rui Wang
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Abstract

In this paper, we investigate the order types of reflection orders on irreducible affine Weyl groups. We show that they are intimately related to the Catalan combinatorics. We explicitly describe all of those order types and show that these order types can be parameterized by deformed Dyck words, which can be enumerated by Catalan numbers.

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Weijia Wang, Rui Wang. 2023-01-25. Order types of reflection orders on affine Weyl groups. https://arxiv.org/abs/2301.10457

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