The spectral decomposition of regular Uq(sl_2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given nearest neighbour spin chain Hamiltonian. The algorithm is based on reduction of the Yang-Baxter equation to certain subspaces. As an application, the complete list of inequivalent regular Uq(sl_2)-invariant R-matrices is obtained for generic q and spins up to s=3/2. Some further results about spectral decompositions for higher spins are also obtained. In particular, it is proved that certain types of regular sl_2-invariant R-matrices have no Uq(sl_2)-invariant counterparts.
Invariants of links with flat connections in their complements.II. Holonomy R-matrices related to quantized universal enveloping algebras at roots of 1
S and T matrices for the super $U(1,1)$ WZW model. Application to surgery and 3-manifold invariants based on the Alexander Conway polynomial
本文从量子场论的角度出发，从\cite{RS91}出发，对Alexander Conway不变量进行了研究。我们首先详细讨论了$U(1,1)$ super WZW模型的$S$和$T$矩阵，并对$k$为整数的模群给出了新的有限维表示.这些具有显著的性质，即某些$S$矩阵元素是无限的。此外，典型的和非典型的表示，以及不可分解的块是混合的：截断到最大的非典型表示，在最近的一些论文中主张，是不一致的。这项工作的主要拓扑应用是亚历山大不变量的3流形和3流形中的链接的计算。3-流形的不变量看起来对$k$水平的依赖很小，但仍然包含有趣的拓扑信息。例如，对于塞弗特流形，它们与第一同调群的阶一致。给出了三维流形中链环不变量的例子。它们表现出有趣的算术性质。
