C_3型仿射Weyl群的左胞腔图和特异对合元图  

Left Cells Graph and Distinguished Involution Graph of the Affine Weyl Group of Type C_3

作　　者：冯鸽[1] 王利萍[1] Feng Ge Wang Liping(School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044)

机构地区：[1]北京建筑大学理学院,北京100044

出　　处：《北京建筑大学学报》2017年第1期53-58,共6页Journal of Beijing University of Civil Engineering and Architecture

基　　金：国家自然科学基金项目(11101233)

摘　　要：特异对合元在Kazhdan-Lusztig理论中具有重要的意义,它们和Weyl群的胞腔分解理论以及Kazhdan-Lusztig多项式的首项系数都有着密切联系.对C_3型仿射Weyl群W进行研究,文献[1]和文献[2]分别给出了W的双边胞腔分解和左胞腔分解.我们首先给出了该情形的基本支配权在相应的扩张仿射Weyl群W中所对应的群元素表示.其次给出了W的左胞腔图及特异对合元图,并借助Kazhdan-Lusztig多项式,对特异对合元进行了验证.In this paper, the distinguished involutions due to their importance in Kazhdan-Lusztig theory are studied. Let W be the affine Weyl group of type C3 whose two-sided cells and left cells are given in [ 1 ] and [2 ] , respectively. The representations of the elements in W corresponding to the fundamental dominant weights are giren. Then the graphs of left cells and distinguished involutions of W are given. Meanwhile, the distinguished involutions obtained by the polynomials of Kazhdan-Lusztig are checked.

关 键 词：仿射WEYL群 特异对合元 双边胞腔 左胞腔 

分 类 号：O153[理学—数学]