On 𝑞-Isomonodromic Deformations and 𝑞-Nekrasov Functions

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 → 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 ∞, we obtain several determinantal identities of the tau functions.