$(q,t)$-deformed (skew) Hurwitz $τ$-functions Article Swipe

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Fan Liu , A. Mironov , V. Mishnyakov , A. Morozov , A. Popolitov , Rui Wang , Wei‐Zhong Zhao ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2303.00552

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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Skew Operator (biology) Mathematics Commutative property Pure mathematics Algebra over a field Rotation (mathematics) Order (exchange) Deformation (meteorology) Geometry Physics Chemistry Economics Astronomy Biochemistry Finance Meteorology Transcription factor Repressor Gene

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2303.00552
PDF: https://arxiv.org/pdf/2303.00552
OA Status: green
Cited By: 4
Related Works: 10
OpenAlex ID: https://openalex.org/W4322825291

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DOI: https://doi.org/10.48550/arxiv.2303.00552

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Title: $(q,t)$-deformed (skew) Hurwitz $τ$-functions

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-03-01

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Authors: Fan Liu, A. Mironov, V. Mishnyakov, A. Morozov, A. Popolitov, Rui Wang, Wei‐Zhong Zhao

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Landing page: https://arxiv.org/abs/2303.00552

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PDF URL: https://arxiv.org/pdf/2303.00552

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Concepts: Skew, Operator (biology), Mathematics, Commutative property, Pure mathematics, Algebra over a field, Rotation (mathematics), Order (exchange), Deformation (meteorology), Geometry, Physics, Chemistry, Economics, Astronomy, Biochemistry, Finance, Meteorology, Transcription factor, Repressor, Gene

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Cited by: 4

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