标题： SU(N) 积分和tau函数 显示英文标题

标题： SU(N) integrals and tau functions

摘要： 我们提出了一类与任意嵌入图$\Gamma$相关的可解多矩阵模型，该图只有一个顶点。 边数为$n$的图配备了$2n$个角矩阵。 该族中每个成员的划分函数依赖于对偶图$\Gamma^*$的顶点周围角矩阵单值群的特征值集合以及附加到$\Gamma$顶点的参数集合。 我们选择划分函数是KP、2KP和BKP层次的tau函数的模型情况。 我们比较关于${U}(N)$和关于${SU}(N)$群的积分。 在$U(N)$情况下，对$\Gamma$的顶点数量没有限制。 显示英文摘要

摘要： We present a family of solvable multi-matrix models associated with an arbitrary embedded graph $\Gamma$ with a single vertex. The graph with $n$ edges is equipped with $2n$ corner matrices. The partition function of each member of the family depends on the set of eigenvalues of monodromies of corner matrices around the vertices of the dual graph $\Gamma^*$ and sets of parameters attached to each vertex of $\Gamma$. We select the cases where the partition function of a model is a tau function of KP, 2KP and BKP hiearachies. We compare integrals over ${U}(N)$ and over ${SU}(N)$ groups. In $U(N)$ case there is no restriction on the number of vertices of $\Gamma$.