Higher-rank isomonodromic deformations and W-algebras

Pavlo Gavrylenko, Nikolai Iorgov, Oleg Lisovyy

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We construct the general solution of a class of Fuchsian systems of rank N as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of WN-algebra with central charge c= N- 1. The simplest example is given by the tau function of the Fuji–Suzuki–Tsuda system, expressed as a Fourier transform of the 4-point conformal block with respect to intermediate weight. Along the way, we generalize the result of Bowcock and Watts on the minimal set of matrix elements of vertex operators of the WN-algebra for generic central charge and prove several properties of semi-degenerate vertex operators and conformal blocks for c= N- 1.

Original languageEnglish
Pages (from-to)327-364
Number of pages38
JournalLetters in Mathematical Physics
Issue number2
Publication statusPublished - 1 Feb 2020


  • Conformal field theory
  • Isomonodromic deformations
  • W-algebras


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