论文标题
在$ \ mathsf {ad} $ - 表示和Vogel参数的立方体中的简单谎言代数的拆分Casimir操作员
Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters
论文作者
论文摘要
我们为伴随表示中的Simple Lie代数的3分（极化）Casimir操作员构建了特征性，并在$ \ Mathsf {ad aD}^{\ otimes 3} $中推导了一类的子陈述。这些子代理的不变子空间的投影仪是由3级Casimir操作员的特征性格直接构建的。对于所有简单的谎言代数，发现了3级Casimir运算符的较高功能的通用表达式，并计算了$ \ Mathsf {ad}^{\ otimes 3} $中子表示的尺寸。我们所有的公式都与$ \ Mathsf {ad}^{\ otimes 3} $中的（不可约）子分量的通用描述一致，以vogel参数为简单代数。
We constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations $\mathsf{ad}$ and deduced a certain class of subrepresentations in $\mathsf{ad}^{\otimes 3}$. The projectors onto invariant subspaces for these subrepresentations were directly constructed from the characteristic identities for the 3-split Casimir operators. For all simple Lie algebras, universal expressions for the traces of higher powers of the 3-split Casimir operators were found and dimensions of the subrepresentations in $\mathsf{ad}^{\otimes 3}$ were calculated. All our formulas are in agreement with the universal description of (irreducible) subrepresentations in $\mathsf{ad}^{\otimes 3}$ for simple Lie algebras in terms of the Vogel parameters.
