W-图理想理论的注记  

Remarks on the Theory of W-graph Ideals

作　　者：殷允川 曹笑丹 Yun Chuan YIN;Xiao Dan CAO(School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,P.R.China)

机构地区：[1]上海财经大学数学学院,上海200433

出　　处：《数学学报（中文版）》2024年第1期173-186,共14页Acta Mathematica Sinica：Chinese Series

摘　　要：本文进一步发展Coxeter系统(W,S)中的W-图理想理论,主要研究与W-图理想相应的Hecke代数上模的结构系数及典范基元素的直接迭代算法.当计算特定典范基元素时,该算法相比标准递推算法具有计算快速节省内存的优势.由于W-图理想概念的广义性,本文的结果也是一些经典情形的推广.We further develop the theory of W-graph ideals in a Coxeter system(W,S).We mainly study the structural coeficients of the corresponding modules,the direct and iterative algorithms for the canonical basis elements.Compared with standard recursive algorithms,this algorithm has the advantage of fast computation and memory saving when computing specific canonical basis elements.Due to the generality of the concept of W-graph ideal,our results are also the generalizations of those in some classical cases.

关 键 词：COXETER群 HECKE代数 W-图理想 典范基 

分 类 号：O152.6[理学—数学]