Partial orders generalizing the weak order on Coxeter groups

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:102

Article

Bennett, CD ; Blok, RJ

关键词: weak order;    Bruhat order;    T-order;    coxeter group;    flag manifold;    Pieri formula;   

DOI  :  10.1016/S0097-3165(03)00046-3

来源: Elsevier

【 摘 要 】

We define a new family of partial orders generalizing the weak order on Coxeter groups called T-orders, where T is a set of reflections determining the covers in this order. We show that the Grassmann and Lagrange orders on the Coxeter groups of type A, and B, introduced by Bergeron and Sottile are in fact T-orders. These partial orders were used to compute certain products in the cohomology ring of the flag manifolds associated to the complex Chevalley groups of these types. We exhibit T-orders generalizing these orders to partial orders for the Coxeter groups of type D-n, E-6, and E-7. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free