论文标题
$ osp（m | n）$和$ s \ ell（m | n）$ lie superalgebras，更高的casimir操作员和vogel参数
The split Casimir operator and solutions of the Yang-Baxter equation for the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras, higher Casimir operators, and the Vogel parameters
论文作者
论文摘要
我们在$ osp（m | n）$和$ s \ ell（m | n）$ lie superalgebras的定义和伴随表示中找到了分裂Casimir操作员的特征性。这些身份用于在表示$ osp（m | n）$和$ s \ ell（m | n）$的$ t^{\ otimes 2} $不变子空间上构建投影仪。为了定义表示形式，$ osp（m | n）$ - 和$ s \ ell（m | n）$ - 杨巴克斯特方程的不变解决方案表示为拆分卡西米尔操作员的合理功能。对于伴随表示，通过Vogel参数化，从谎言超级级别的普遍描述的角度考虑了获得的特征身份和不变投影仪。我们还为$ osp（m | n）$和$ s \ ell（m | n）$ lie superalgebras的高级Casimir运营商构建了通用生成功能。
We find the characteristic identities for the split Casimir operator in the defining and adjoint representations of the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras. These identities are used to build the projectors onto invariant subspaces of the representation $T^{\otimes 2}$ of the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras in the cases when $T$ is the defining and adjoint representations. For defining representations, the $osp(M|N)$- and $s\ell(M|N)$-invariant solutions of the Yang-Baxter equation are expressed as rational functions of the split Casimir operator. For the adjoint representation, the characteristic identities and invariant projectors obtained are considered from the viewpoint of a universal description of Lie superalgebras by means of the Vogel parametrization. We also construct a universal generating function for higher Casimir operators of the $osp(M|N)$ and $s\ell(M|N)$ Lie superalgebras in the adjoint representation.
