论文标题
使用$ w_ {1+ \ infty} $运算符的GKM的有序指数表示
The ordered exponential representation of GKM using the $W_{1+\infty}$ operator
论文作者
论文摘要
广义的Kontsevich模型（GKM）是一个具有任意潜力的单矩阵模型。它的分区函数属于KP层次结构。当潜力是单一的时，它是$ r $ $ $ $ r $ r $ $ -SPIN的交集数字的功能。在本文中，我们以$ w_ {1+\ infty} $操作员的身份提出了单个GKM的有序指数表示，该指数表示可保留KP集成性。实际上，此表示自然是$ w_ {1+ \ infty} $约束的解决方案，该解决方案唯一地决定了tau功能。此外，我们表明，对于Kontsevich-witten和Permarized BGW Tau功能的情况，在减少时间独立性和Virasoro收藏量的减少下，可以将其$ w_ {1+ \ infty} $表示。
The generalized Kontsevich model (GKM) is a one-matrix model with arbitrary potential. Its partition function belongs to the KP hierarchy. When the potential is monomial, it is an $r$-reduced tau-function that governs the $r$-spin intersection numbers. In this paper, we present an ordered exponential representation of monomial GKM in terms of the $W_{1+\infty}$ operators that preserves the KP integrability. In fact, this representation is naturally the solution of a $W_{1+\infty}$ constraint that uniquely determines the tau-function. Furthermore, we show that, for the cases of Kontsevich-Witten and generalized BGW tau-functions, their $W_{1+\infty}$ representations can be reduced to their cut-and-join representations under the reduction of the even time independence and Virasoro constraints.
