Isomonodromic deformations: confluence, reduction and quantisation

Ilia Gaiur, Marta Mazzocco, Vladimir Rubtsov

Research output: Working paper/PreprintPreprint

117 Downloads (Pure)

Abstract

In this paper we study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-adjoint orbits of the Takiff algebra (i.e. truncated current algebra). Our motivation is to produce confluent versions of the celebrated Knizhnik–Zamolodchikov equations and explain how their quasiclassical solution can be expressed via the isomonodromic τ-function. In order to achieve this, we study the confluence cascade of r + 1 simple poles to give rise to a singularity of arbitrary Poincaré rank r as a Poisson morphism and explicitly compute the isomonodromic Hamiltonians.
Original languageEnglish
Publication statusPublished - 25 Jun 2021

Bibliographical note

51 pages, 3 figures

Keywords

  • math.AG
  • math-ph
  • math.MP
  • 32G34, 17B37, 17B63, 53D17, 34M56

Fingerprint

Dive into the research topics of 'Isomonodromic deformations: confluence, reduction and quantisation'. Together they form a unique fingerprint.

Cite this