Q-deformed Painleve tau function and q-deformed conformal blocks
Abstract
We propose q-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev\'e τ function. Namely we propose formula for τ function for q-difference Painlev\'e equation corresponding to A7(1)' surface (and A1(1) symmetry) in Sakai's classification. In this formula τ function equals the series of q-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure SU(2) 5d theory).
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