Some cells in the weighted Coxeter group ((c)over-tilden,(l)over-tilde2n+1)

JOURNAL OF ALGEBRA

卷:395

Article

Huang, Qian¹  Shi, Jian-yi¹ 

[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

关键词: Affine Weyl groups;    Left cells;    Two-sided cells;    Quasi-split case;    Weighted Coxeter group;   

DOI  :  10.1016/j.jalgebra.2013.08.002

来源: Elsevier

【 摘 要 】

The fixed point set of the Milne Weyl group ((A)over tilde>(2n+1),(S)over tilde>) under a certain group automorphism a with alpha ((S)over tilde>) = (S)over tilde> can be considered as the affine Weyl group ((c)over tilde>(n),S). Then we study the cells of the weighted Coxeter group ((c)over tilde>(n),(l)over tilde>(2n+1)) with (A)over tilde>(2n+1) the length function of (c)over tilde>(2n+1). We give an explicit description for all the cells of ((c)over tilde>n,(c)over tilde>(2n+1)) corresponding to the partitions k1(2n+2-k) and (h, 2n + 2 - h) for any 1 <= k <= 2n + 2 and n+1.<= h <= 2n, and also for all the cells of (c)over tilde>(3) (l)over tilde>(7)). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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