On monomial linearisation and supercharacters of pattern subgroups

作     者：Qiong Guo Richard Dipper 

作者机构：College of Sciences Shanghai Institute of Technology Shanghai 201418 China Institut fur Algebra und Zahlentheorie Universitat Stuttgart Stuttgart 70569 Germany 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第2期

页      面：227-252页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11601338) the German Research Foundation,Priority Programme Deutsche ForschungsgemeinschaftSchwerpunktsprogramm Darstellungstheorie 1388 in Representation Theory(Grant No.99028426) 

主　　题：column closed subgroups monomial linearisation supercharacter 

摘      要：Column closed pattern subgroups U of the finite upper unitriangular groups U_n(q) are defined as sets of matrices in U_n(q) having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky s construction of monomial linearisation in his thesis and apply this to CU yielding a generalisation of Yan s coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters,by describing the resulting orbits and determining the Hom-spaces between orbit modules.