Two programs to perform certain symbolic calculations in the enveloping algebra of a lie algebra

Title of program: ORDINVAR Catalogue Id: AATP_v1_0 Nature of problem To find explicit expressions (in standard order) for the invariants of a Lie algebra, i.e. for the polynomials in the generators which commute with all generators. An appropriate choice for the Lie algebra basis and for the order of the generators in standard form, leads to algebraic closed formulae for the eigenvalues of the generalized Casimir operators upon highest weight states of irreducible representations. Versions of this program held in the CPC repository in Mendeley Data AATP_v1_0; ORDINVAR; 10.1016/0010-4655(87)90027-0 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)程序名称：ORDINVAR 目录编号：AATP_v1_0 问题描述：本程序旨在求解李代数（Lie algebra）不变量的标准序显式表达式，即所有生成元均与之可交换的生成元多项式。通过合理选取李代数基矢以及生成元的标准序形式，可针对不可约表示（irreducible representations）的最高权态，推导出广义卡西米尔算子（generalized Casimir operators）本征值的代数闭合公式。 本程序收录于Mendeley数据平台的CPC程序库中，对应版本为AATP_v1_0；关联标识：ORDINVAR；文献DOI：10.1016/0010-4655(87)90027-0 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）。