论文标题
量子kac-moody代数的通用k-矩阵
Universal K-matrices for quantum Kac-Moody algebras
论文作者
论文摘要
我们介绍了一个圆柱式双方的概念，该圆柱型是一种准二晶型双子$ h $，赋予了通用k-matrix的元素，即通用反射方程的通用解决方案，产生了圆柱形编织组对其表示的Tensor产品的作用。我们证明，这种通用K-诊断的新示例来自KAC-MOODY类型的量子对称对，并取决于选择一对普遍的Satake图。在有限的类型中，这得出了Balagović和Kolb获得的结果的完善，并产生了最初是由于BAO和Wang和Full unisial K-Matrix在准K-Matrix之间插值的非等效溶液家族。最后，我们证明，在量子仿射代数$ u_ql \ mathfrak {sl} _2 _2 $的情况下，这种构造产生了具有光谱参数的广义反射方程的正式解决方案。
We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra $H$ endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection equation, yielding an action of cylindrical braid groups on tensor products of its representations. We prove that new examples of such universal K-matrices arise from quantum symmetric pairs of Kac-Moody type and depend upon the choice of a pair of generalized Satake diagrams. In finite type, this yields a refinement of a result obtained by Balagović and Kolb, producing a family of non-equivalent solutions interpolating between the quasi-K-matrix originally due to Bao and Wang and the full universal K-matrix. Finally, we prove that this construction yields formal solutions of the generalized reflection equation with a spectral parameter in the case of finite-dimensional representations over the quantum affine algebra $U_qL\mathfrak{sl}_2$.
