G_2型Shi-Catalan构形的自由性  

The freeness of Shi-Catalan arrangements of type G_2

作　　者：高瑞梅[1] 

机构地区：[1]长春理工大学理学院,吉林长春130022

出　　处：《山东大学学报（理学版）》2014年第12期66-70,94,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11271063;11326078);黑龙江省教育厅科技研究项目(12531187)

摘　　要：G2型Shi-Catalan构形是二维空间中的重构形,它是将G2型Weyl构形在同一轨道中的超平面赋予相同的重数而得到的构形。给出了G2型Shi-Catalan构形的4种具体形式,通过将构形投影到射影平面计算构形中超平面交点个数的方法,证明了G2型Shi-Catalan构形的锥构形都是自由的。The Shi-Catalan arrangements of type G2 are multiarrangements in the 2-dimensional vector space, which are obtained by giving the same multiplicity to the hyperplanes in the same orbit in Weyl arrangements of type G2. Four concrete forms of Shi-Catalan arrangements of type G2 are given. By counting the intersections of hyperplanes in reflec- tion planes, we prove the conclusion that the cones over the Shi-Catalan arrangements of type G2 are all free.

关 键 词：Weyl构形 Shi—Catalan构形 自由性 

分 类 号：O189[理学—数学]