Q-deformed Painleve tau function and q-deformed conformal blocks
Bershtein, M. A. ; Shchechkin, A. I.
arXiv, 1608.02566 / Harvested from arXiv
Text on arXiv
We propose $q$-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev\'e $\tau$ function. Namely we propose formula for $\tau$ function for $q$-difference Painlev\'e equation corresponding to $A_7^{(1)}{}'$ surface (and $A_1^{(1)}$ symmetry) in Sakai's classification. In this formula $\tau$ function equals the series of $q$-Virasoro Whittaker conformal blocks (equivalently Nekrasov partition functions for pure $SU(2)$ 5d theory).
Publié le : 2016-08-08
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Mathematics - Quantum Algebra,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{1608.02566,
     author = {Bershtein, M. A. and Shchechkin, A. I.},
     title = {Q-deformed Painleve tau function and q-deformed conformal blocks},
     journal = {arXiv},
     volume = {2016},
     number = {0},
     year = {2016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1608.02566}
}

Bershtein, M. A.; Shchechkin, A. I. Q-deformed Painleve tau function and q-deformed conformal blocks. arXiv, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/1608.02566/