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

M. A. Bershtein, A. I. Shchechkin

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


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).

Original languageEnglish
Article number085202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
Publication statusPublished - 23 Jan 2017


  • bilinear equations
  • difference Painleve equations
  • Nekrasov partition functions
  • Sakai's classification


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