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Painlevé equations from Nakajima–Yoshioka blowup relations

Bershtein M.
•
Shchechkin A.
2019
  • journal article

Periodico
LETTERS IN MATHEMATICAL PHYSICS
Abstract
Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé equation is equal to the series of c= 1 Virasoro conformal blocks. We study similar series of c= - 2 conformal blocks and relate it to Painlevé theory. The arguments are based on Nakajima–Yoshioka blowup relations on Nekrasov partition functions. We also study series of q-deformed c= - 2 conformal blocks and relate it to q-Painlevé equation. As an application, we prove formula for the tau function of q-Painlevé A7(1)′ equation.
DOI
10.1007/s11005-019-01198-4
WOS
WOS:000490945600001
Archivio
https://hdl.handle.net/20.500.11767/147051
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85070260644
https://arxiv.org/abs/1811.04050
Diritti
open access
license:non specificato
license:non specificato
license uri:na
license uri:na
Soggetti
  • Bilinear relations

  • Blowup relations

  • Conformal blocks

  • Nekrasov partition fu...

  • Painleve equations

  • q-difference equation...

  • Settore MATH-04/A - F...

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