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量子仿射（超）代数$U_q(A_{1}^{(1)})$和$U_q(C(2)^{(2)})$

Quantum Affine (Super)Algebras $U_q(A_{1}^{(1)})$ and $U_q(C(2)^{(2)})$

S. M. Khoroshkin, J. Lukierski, V. N. Tolstoy

备注：
22 pages, LaTeX
发表信息：
Commun.Math.Phys. 220 (2001) 537-560
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摘要：

证明了量子仿射代数$U_{q}(A_{1}^{(1)})$和量子仿射超代数$U_{q}(C(2)^{(2)})$具有统一的描述.它们之间的差异在于相位因子，对于$U_{q}(A_{1}^{(1)})$，相位因子等于1，对于$U_{q}(C(2)^{(2)})$，相位因子等于-1。我们给出了辫群作用的描述，Cartan-Weyl生成元及其对易关系的构造，极值投影和泛R-矩阵的描述.我们还给出了这些代数的“新实现”的统一描述以及相应R-矩阵的显式计算。

英文摘要：

We show that the quantum affine algebra $U_{q}(A_{1}^{(1)})$ and the quantum affine superalgebra $U_{q}(C(2)^{(2)})$ admit a unified description. The difference between them consists in the phase factor which is equal to 1 for $U_{q}(A_{1}^{(1)})$ and it is equal to -1 for $U_{q}(C(2)^{(2)})$. We present such a description for the actions of the braid group, for the construction of Cartan-Weyl generators and their commutation relations, as well for the extremal projector and the universal R-matrix. We give also a unified description for the 'new realizations' of these algebras together with explicit calculations of corresponding R-matrices.

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