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$(q,t)$-deformed (skew) Hurwitz $\tau$-functions

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arxiv 2303.00552 v2 pith:6XDC457P submitted 2023-03-01 hep-th math-phmath.MP

Fan Liu , A. Mironov , V. Mishnyakov , A. Morozov , A. Popolitov , Rui Wang , Wei-Zhong Zhao This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords deformationdifferencefunctionsmacdonaldoperatoroperatorstermsalgebra
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abstract

We follow the general recipe for constructing commutative families of $W$-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a $(q,t)$-deformation of the earlier studied models. As before, a key role is played by an appropriate deformation of the cut-and-join rotation operator. We outline its expression both in terms of generators of the quantum toroidal algebra and in terms of the Macdonald difference operators.

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  1. Phases in WLZZ Matrix Models

    hep-th 2025-07 conditional novelty 6.0 of 10

    For WLZZ two-matrix models, integration contours describe only a finite-N subspace of Ward identity solutions, and the full solution space is recovered only in the N-to-infinity limit.

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