论文标题
Tensor Harish-Chandra-Itzykson-Zuber Integral I：Weingarten演算和单调Hurwitz数字的概括
The tensor Harish-Chandra-Itzykson-Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers
论文作者
论文摘要
我们研究了Harish -Chandra -Itzykson的概括 - Zuber与张量的积分不可或缺的积分及其对两个外部张量的痕量不变的扩展。这引起了单调双Hurwitz数字的自然概括，这些数字计算了某些星座家庭。我们发现这些数字的表达方式是单调简单的Hurwitz数字，从而提供了单调双Hurwitz数量的单个任意属的表达式。我们用nodal表面的枚举来解释不同组合数量的作用。特别是，我们对Hurwitz数字的概括被证明是列举了一束$ D $ 2 $ 2秒的花束覆盖物的某些同构类别类，这些覆盖物与一个常见的非分支节点触摸。
We study a generalization of the Harish-Chandra - Itzykson - Zuber integral to tensors and its expansion over trace-invariants of the two external tensors. This gives rise to natural generalizations of monotone double Hurwitz numbers, which count certain families of constellations. We find an expression of these numbers in terms of monotone simple Hurwitz numbers, thereby also providing expressions for monotone double Hurwitz numbers of arbitrary genus in terms of the single ones. We give an interpretation of the different combinatorial quantities at play in terms of enumeration of nodal surfaces. In particular, our generalization of Hurwitz numbers is shown to enumerate certain isomorphism classes of branched coverings of a bouquet of $D$ 2-spheres that touch at one common non-branch node.
