The tensor Harish-Chandra-Itzykson-Zuber integral: I. Weingarten calculus and a generalization of monotone Hurwitz numbers
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 expres...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
25 Jan 2022
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| Edition: | Version v2 |
| In: |
Arxiv
Year: 2020, Pages: 1-43 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2010.13661
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| Author Notes: | Benoît Collins, Razvan Gurau, Luca Lionni |
| Summary: | 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. |
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| Item Description: | Version 1 vom 26. Oktober 2020, Version 2 vom 25. Januar 2022 Gesehen am 05.10.2022 |
| Physical Description: | Online Resource |