黑克、布劳、及伯曼-温采尔代数的诱导及分导系数和量子经典李代数的耦合与重新耦合系数

本文总结了计算黑克、布劳、及伯曼 温采尔代数在各种工数链下诱导及分导系数的线性方程方法(LEM)。特别强调了关于A,B,C,D型李代数及其量子情形与其中心代数之间的舒尔 魏尔 布劳双关性关系。这一关系使我们能够利用相应中心代数的诱导及分导系数计算出经典李代数及其量子情形的耦合与重新耦合系数。讨论了从该方法得到B,C,D型李代数不可约表示克罗内克积分解的应用。基于LEM还得到了处理对应于置换群CG系列问题的黑克代数张量积的方法。

Induction and subduction coefficients of Hecke,Brauer,and Birman-Wenzl algebras and coupling and re-coupling coefficients of quantum and classical Lie algebras

The Linear Equation Method (LEM) for evaluating induction and subduction coefficients of Hecke, Brauer, and Birman_Wenzl algebras in various algebraic chains is reviewed. The Schur_Weyl_Brauer duality relation between A,B,C, and D type of Liealgebras and their centralizer algebras, and its quantum version is emphasized. The relation allows us to evaluate coupling and re_coupling coefficients of the corresponding quantum and classical Lie algebras from the induction and subduction coefficients of their centralizer algebras. Applications to the decomposition of Kronecker products for irreducible representations of the B, C, D type Lie algebras are also outlined. A procedure for dealing with tensor products of Hecke algebras, which corresponds to the CG series of permutation groups, are also formulated based on the LEM.