On W-operators and superintegrability for dessins d'enfant
Alexander Alexandrov
TL;DR
This paper links a family of partition functions to dessins d'enfant, revealing new superintegrability examples in matrix models and offering a W-operator perspective for orbifold Hurwitz numbers.
Contribution
It introduces a novel W-operator framework for orbifold Hurwitz numbers and connects partition functions to dessins d'enfant generating functions.
Findings
Identifies a family of partition functions with dessins d'enfant generating functions
Provides new superintegrability examples in matrix models
Offers a W-operator description for orbifold Hurwitz numbers
Abstract
In this short note we identify a family of partition functions recently introduced by Wang, Liu, Zhang, and Zhao with certain specializations of the generating function for dessins d'enfant. This provides a new W-description for orbifold strongly monotone Hurwitz numbers and new examples of superintegrability in matrix models.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Mathematical Identities