Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (6): 1-13.doi: 10.3969/j.issn.1000-5641.2023.06.001

• Mathematics •    

A survey on the cell theory of weighted Coxeter groups

Jianyi SHI1(), Qian HUANG2   

  1. 1. School of Mathematical Sciences, East China Normal University, Shanghai 200241, China
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
  • Received:2023-06-01 Online:2023-11-25 Published:2023-11-23

Abstract:

We give a survey on the contribution of our research group to the cell theory of weighted Coxeter groups. We present some detailed account for the description of cells of the affine Weyl group $ \widetilde{C}_n $ in the quasi-split case and a brief account for that of the affine Weyl group $ \widetilde{B}_n $ in the quasi-split case and of the weighted universal Coxeter group in general case.

Key words: affine Weyl group, weighted Coxeter group, quasi-split case, cells, partitions, tabloids

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