量子对称对的泛K-矩阵
Universal K-matrix for quantum symmetric pairs
摘要：
设$\mathfrak{g}$是可对称化的Kac-Moody代数，$U_q(\mathfrak{g})$表示相应的量化包络代数.本文证明了当$\mathfrak{g}$为有限型时，$U_q(\mathfrak{g})$的量子对称对偶余理想子代数$B_{c,s}$具有泛K-矩阵. $B_{c,s}$的泛K-矩阵是指$U_q(\mathfrak{g})$的完备化中的一个元素，它与$B_{c,s}$交换，并提供反射方程在范畴$\mathcal{O}$中所有可积$U_q(\mathfrak{g})$ -模中的解。$B_{c,s}$的泛K-矩阵的构造与$U_q(\mathfrak{g})$的泛R-矩阵的构造有很大的相似性。构造泛K矩阵的大多数步骤都是在一般的Kac-Moody设置中执行的。90年代末，T。tom Dieck和R. Häring-Oldenburg开发了一个表示圆柱体中带状物类别的程序。我们的研究结果表明，量子对称对提供了一个大类的例子，这个程序。
英文摘要：
Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra and let $U_q(\mathfrak{g})$ denote the corresponding quantized enveloping algebra. In the present paper we show that quantum symmetric pair coideal subalgebras $B_{c,s}$ of $U_q(\mathfrak{g})$ have a universal K-matrix if $\mathfrak{g}$ is of finite type. By a universal K-matrix for $B_{c,s}$ we mean an element in a completion of $U_q(\mathfrak{g})$ which commutes with $B_{c,s}$ and provides solutions of the reflection equation in all integrable $U_q(\mathfrak{g})$-modules in category $\mathcal{O}$. The construction of the universal K-matrix for $B_{c,s}$ bears significant resemblance to the construction of the universal R-matrix for $U_q(\mathfrak{g})$. Most steps in the construction of the universal K-matrix are performed in the general Kac-Moody setting. In the late nineties T. tom Dieck and R. Häring-Oldenburg developed a program of representations of categories of ribbons in a cylinder. Our results show that quantum symmetric pairs provide a large class of examples for this program.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
