Article ID Journal Published Year Pages File Type
4588308 Journal of Algebra 2008 25 Pages PDF
Abstract

We introduce two methods which reduce the checking of the joint relations on element pairs x,y (i.e., checking if μ(x,y)≠0, see 1.2) inside a two-sided cell of the symmetric group Sn to some special cases up to star operations. One involves the involutions in Sn, and the other involves the set Σλ for λ∈Λn (see 3.1 and 5.1). We give a detailed investigation for the properties of the set Σλ in terms of standard tableaux. Also, we study the sets U(S∞) and U′(S∞) and give an affirmative answer to a question of N.H. Xi (see Proposition 2.9).

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory