The cells in the weighted Coxeter group ((C)over-tilden, (l)over-tildem)

JOURNAL OF ALGEBRA

卷:443

Article

Shi, Jian-yi

关键词: Affine Weyl group;    Weighted Coxeter group;    Quasi-split case;    Left cell;    Two-sided cell;    Partition;    Tabloid;    k-circle;   

DOI  :  10.1016/j.jalgebra.2015.06.044

来源: Elsevier

【 摘 要 】

The affine Weyl group ((C) over tilde (n), S) can be realized as the fixed point set of the affine Weyl group ((A) over tilde (m),(S) over tilde (m)), m is an element of {2n - 1, 2n, 2n + 1}, under a certain group automorphism alpha(m,n). Let l(m) be the length function of (A) over tilde (m). The aim of the present paper is to give a combinatorial description for all the left cells of (A) over tilde (m) which have non-empty intersection with (C) over tilde (n). Then we use this description to deduce some formulae for the number of left cells of the weighted Coxeter group ((C) over tilde (n), (l) over tilde (m)) in the set E-lambda associated to any partition lambda of m + 1. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free