A_l型Weyl群子根系轨道生成的格

Lattices Generated by Transitive Sets of Root Subsystems Under Weyl Groups of A_l

利用W ey l群的性质及置换理论,讨论了Al型W ey l群作用下的子根系轨道生成的格.在同类型格中,研究了不同格之间的包含关系,给出了一个子根系是给定由μ生成的格L(μ)中一个元素的条件,最后讨论了按包含关系或反包含关系规定L(μ)的偏序时,L(μ)是否为几何格.

The lattice generated by transitive sets of root subsystems under Weyl groups of type Al was studied. Let L（μ） be a lattice generated by μ. At first the inclusion relations between the lattices of the same type is studied. Then the condition of root subsystems contained in a given lattice was listed. Finally, the geometrical properties of the lattices were described.