The 2-Component BKP Grassmannian and Simple Singularities of Type D
The 2-Component BKP Grassmannian and Simple Singularities of Type D
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DOI：
10.1093/imrn/rnz325
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发表时间：
2018-04
影响因子：
1
通讯作者：
Jipeng Cheng;T. Milanov
中科院分区：
文献类型：
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作者：
Jipeng Cheng;T. Milanov
在2010年证明了$D$型的主Kac-Wakimoto族是2-分量BKP族的约化。另一方面，它是已知的，总后裔潜力的一个奇点的类型$D$是一个τ函数的主要Kac-Wakimoto层次。我们明确地找到点在格拉斯曼的2-分量BKP层次结构（在盐田的意义上），对应于总的后代潜力。我们还证明了高斯型τ-函数空间是由D$型简单奇点的极小开折基参数化的。
It was proved in 2010 that the principal Kac–Wakimoto hierarchy of type $D$ is a reduction of the 2-component BKP hierarchy. On the other hand, it is known that the total descendant potential of a singularity of type $D$ is a tau-function of the principal Kac–Wakimoto hierarchy. We find explicitly the point in the Grassmannian of the 2-component BKP hierarchy (in the sense of Shiota) that corresponds to the total descendant potential. We also prove that the space of tau-functions of Gaussian type is parametrized by the base of the miniversal unfolding of the simple singularity of type $D$.