Isomonodromic Deformations: Confluence, Reduction and Quantisation

Abstract In this paper we study the isomonodromic deformations of systems differential equations with poles any order on Riemann sphere as Hamiltonian flows product co-adjoint orbits truncated current algebra, also called generalised Takiff algebra. Our motivation is to produce confluent versions celebrated Knizhnik–Zamolodchikov and explain how their quasiclassical solution can be expressed via $$\tau $$ τ -function. achieve this, confluence cascade $$r+ 1$$ r + 1 simple give rise a singularity arbitrary Poincaré rank r Poisson morphism explicitly compute Hamiltonians. loving memory Igor Krichever A great man outstanding mathematician