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## q-deformed Painlevé τ function and q-deformed conformal blocks

Journal of Physics A: Mathematical and Theoretical. 2017. Vol. 50. No. 8. P. 1-20.

We propose the q-deformation of the Gamayun–Iorgov–Lisovyy formula for the Painlevé τ function. Namely, we propose the formula for the τ function for the q-difference Painlevé equation corresponding to the surface (and the symmetry) in the Sakai classification. In this formula, the τ function equals the series of q-Virasoro Whittaker conformal blocks (equivalently, the Nekrasov partition functions for pure SU(2) 5d theory).