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...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.展开更多
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)
文摘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.
