Joint relations on elements of the symmetric group

JOURNAL OF ALGEBRA

卷:319

Article

Shi, Jian-yi

关键词: symmetric group;    young tableaux;    joint relations;   

DOI  :  10.1016/j.jalgebra.2007.08.018

来源: Elsevier

【 摘 要 】

We introduce two methods which reduce the checking of the joint relations on element pairs x, y (i.e., checking if mu(x, y) not equal 0, see 1.2) inside a two-sided cell of the symmetric group S-n to some special cases up to star operations. One involves the involutions in S-n, and the other involves the set Sigma(lambda) for lambda is an element of Lambda(n) (see 3.1 and 5.1). We give a detailed investigation for the properties of the set Sigma(lambda) in terms of standard tableaux. Also, we study the sets U(S-infinity) and U'(S-infinity) and give an affirmative answer to a question of N.H. Xi (see Proposition 2.9). (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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