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Generic c=1 four-point conformal blocks on the Riemann sphere can be seen as the coefficients of Fourier expansion of the tau function of Painlev\'e VI equation with respect to one of its integration constants.
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B. Ponsot, J. Teschner, Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of 𝒰 q ( 𝔰 𝔩 ( 2 , ℝ ) ) \mathcal{U}_{q}(\mathfrak{sl}(2,\mathbb{R}))
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2003
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2004
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P. P. Boalch, From Klein to Painlevé via Fourier, Laplace and Jimbo
2005
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A. V. Kitaev, Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations
2005
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P. Deift, A. Its, I. Krasovsky, X. Zhou, The Widom-Dyson constant for the gap probability in random matrix theory
2007
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2010
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T. Claeys, A. Its, I. Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V
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2005
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2005
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2006
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2006
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2012
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O. Gamayun, N. Iorgov, O. Lisovyy, Conformal field theory of Painlevé VI
2012
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2013
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