Quantization of simply-laced isomonodromy systems by the quantum spectral curve method

DOI10.55937/sut/1654147040OpenAlexW4285608784MaRDI QIDQ2092314

Daisuke Yamakawa

Publication date: 2 November 2022

Published in: SUT Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.55937/sut/1654147040

zbMATH Keywords

quantizationisomonodromic deformations

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Cites Work

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• Algebraic properties of Manin matrices. I
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem
• Dual isomonodromic deformations and moment maps to loop algebras
• Differential equations compatible with KZ equations
• Simply-laced isomonodromy systems
• Simply-laced quantum connections generalising KZ
• The quantum Gaudin system
• Manin matrices and Talalaev's formula
• Generalized Knizhnik–Zamolodchikov equations and isomonodromy quantization of the equations integrable via the Inverse Scattering Transform: Maxwell–Bloch system with pumping
• Confluent KZ equations for {\mathfrak {sl}}_N with Poincaré rank 2 at infinity

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