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arXiv · 2004.13916

On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions

Hajime Nagoya
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Abstract

We construct a fundamental system of a $q$-difference Lax pair of rank $N$ in terms of 5d Nekrasov functions with $q=t$. Our fundamental system degenerates by the limit $q\to 1$ to a fundamental system of a differential Lax pair, which yields the Fuji-Suzuki-Tsuda system. We introduce tau functions of our system as Fourier transforms of 5d Nekrasov functions. Using asymptotic expansions of the fundamental system at $0$ and $\infty$, we obtain several determinantal identities of the tau functions.

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BibTeXRIS

Hajime Nagoya. 2020-04-29. On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions. https://doi.org/10.3842/sigma.2021.050

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