The relation ≤LR on some elements of the affine Weyl group (C)over-tilden

JOURNAL OF ALGEBRA

卷:479

Article

Shi, Jian-yi¹ 

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

关键词: Affine Weyl group;    The longest element;    Left cell;    Two-sided cell;    Partition;    Iterating star operations;   

DOI  :  10.1016/j.jalgebra.2017.01.024

来源: Elsevier

【 摘 要 】

Let (W, S) be the affine Weyl group of type (C-n) over tilde with S its Coxeter generator set. Let (Lambda(2n+1)) over bar be the set of all partitions lambda = (lambda(1),..., lambda(r)) of 2n + 1 such that Sigma(2k+1)(j=1) lambda(j) is odd for any k is an element of N with 2k + 1 <= r. For any J subset of S, let w(J) be the longest element in the parabolic subgroup of W generated by J. We define a map (phi) over bar : {w(J) vertical bar J subset of S }-> (Lambda(2n+1)) over bar and study the preorder <= (LR)on the set {(phi) over bar (w(J)) vertical bar J subset of S} and its relation with theLR partial order 5 on the set {7(wj) J S}, where iterating star operations and primitive pairs play an important role. (C) 2017 Elsevier Inc. All rights reserved.

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