Geodesic
On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: isomonodromic deformations; Nekrasov functions; Painlevé equations; determinantal identities. 
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     author = {Hajime Nagoya},
     title = {On $q${-Isomonodromic} {Deformations} and $q${-Nekrasov} {Functions}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
     volume = {17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a49/}
}
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Hajime Nagoya. On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a49/

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