TY - JOUR
T1 - Isomonodromic Deformations
T2 - Confluence, Reduction and Quantisation
AU - Gaiur, Ilia
AU - Mazzocco, Marta
AU - Rubtsov, Vladimir
PY - 2023/6
Y1 - 2023/6
N2 - 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 truncated current algebra, also called generalised Takiff 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. In loving memory of Igor Krichever. A great man and outstanding mathematician.
AB - 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 truncated current algebra, also called generalised Takiff 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. In loving memory of Igor Krichever. A great man and outstanding mathematician.
U2 - 10.1007/s00220-023-04650-8
DO - 10.1007/s00220-023-04650-8
M3 - Article
SN - 0010-3616
VL - 400
SP - 1385
EP - 1461
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -