On Ad-Nilpotent b-Ideals for Orthogonal Lie Algebras  

作　　者：Li Li LIU Li LUO 

机构地区：[1]Department of Mathematics,East China Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第2期241-262,共22页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11026103,11101151);Fundamental Research Funds for the Central Universities

摘　　要：Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence hut also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i.e., types B and D.Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence hut also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i.e., types B and D.

关 键 词：Orthogonal Lie algebra Borel subalgebra ad-nilpotent ideal 

分 类 号：O152.5[理学—数学] O153.3[理学—基础数学]