EL-labelings, supersolvability and 0-Hecke algebra actions on posets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:101

Article

McNamara, P

关键词: poset;    lattice;    EL-labeling;    supersolvable lattice;    Hecke algebra action;    quasisymmetric function;   

DOI  :  10.1016/S0097-3165(02)00019-5

来源: Elsevier

【 摘 要 】

It is well known that if a finite graded lattice of rank n is supersolvable, then it has all EL-labeling where the labels along any maximal chain form a permutation. We call such a labeling an S-n EL-labeling and we show that a finite graded lattice of rank n is supersolvable if and only if it has such a labeling. We next consider finite graded posets of rank n with (0) over cap and (1) over cap that have an S-n EL-labeling. We describe a type A 0-Hecke algebra action oil the maximal chains of such posets. This action is local and gives a representation of these Hecke algebras whose character has characteristic that is closely related to Ehrenborg's flag quasisymmetric function. We ask what other classes of posets have such an action and in particular we show that finite graded lattices of rank n have such an action if and only if they have an S-n EL-labeling. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free