The tensor Harish-Chandra–Itzykson–Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers

  • Benoît Collins

    Kyoto University, Japan
  • Razvan Gurau

    Universität Heidelberg, Germany
  • Luca Lionni

    Radboud University, Nijmegen, Netherlands
The tensor Harish-Chandra–Itzykson–Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers cover

A subscription is required to access this article.

Abstract

We study a generalization of the Harish-Chandra–Itzykson–Zuber integral to tensors and its expansion in terms of 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 count certain isomorphism classes of branched coverings of a bouquet of 2-spheres that touch at one common non-branch node.

Cite this article

Benoît Collins, Razvan Gurau, Luca Lionni, The tensor Harish-Chandra–Itzykson–Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1315