## Abstract

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 W_{N}-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 W_{N}-algebra for generic central charge and prove several properties of semi-degenerate vertex operators and conformal blocks for c= N- 1.

Original language | English |
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Pages (from-to) | 327-364 |

Number of pages | 38 |

Journal | Letters in Mathematical Physics |

Volume | 110 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2020 |

## Keywords

- Conformal field theory
- Isomonodromic deformations
- W-algebras