论文标题
与Frobenius歧管的无限家族相关的可集成层次结构
Integrable hierarchies associated to infinite families of Frobenius manifolds
论文作者
论文摘要
我们提出了与任何无限系列的Frobenius歧管相关的可集成层次结构的新结构，以满足一定的稳定条件。我们研究了与$ a_n $，$ d_n $和$ b_n $奇异性相关的Frobenius流形的这些层次结构。在$ a_n $ frobenius的情况下，我们的层次结构与KP层次结构一致；对于$ b_n $ frobenius歧管，它与BKP层次结构一致；对于$ d_n $层次结构，这是对2组件BKP层次结构的一定减少。作为这些结果的附带产品，我们说明了$ a_n $，$ d_n $和$ b_n $ frobenius势的某些系数的枚举含义。
We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to $A_N$, $D_N$ and $B_N$ singularities. In the case of $A_N$ Frobenius manifolds our hierarchy turns out to coincide with the KP hierarchy; for $B_N$ Frobenius manifolds it coincides with the BKP hierarchy; and for $D_N$ hierarchy it is a certain reduction of the 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of $A_N$, $D_N$ and $B_N$ Frobenius potentials.
