Simply-Laced Quantum Connections Generalising KZ

• Published in: Communications in mathematical physics Vol. 368; no. 1; pp. 1 - 54
• Main Author: Rembado, Gabriele
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2019; Springer Nature B.V; Springer Verlag
• Subjects: Algebraic Geometry; Classical and Quantum Gravitation; Complex Systems; Deformation; Differential Geometry; Geometric Topology; Group Theory; Hamiltonian functions; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Physics; Physics and Astronomy; Quantum Algebra; Quantum Physics; Relativity Theory; Rings and Algebras; Symplectic Geometry; Theoretical; Time dependence; 2022. 2010 Mathematics Subject Classification. 81R12 Isomonodromic deformations; meromorphic connections; quantum integrable systems; August 9; deformation quantisation; quiver varieties

We construct a new family of flat connections generalising the KZ connection, the Casimir connection and the dynamical connection. These new connections are attached to simply-laced graphs, and are obtained via quantisation of time-dependent Hamiltonian systems controlling the isomonodromic deformat...