Simply-Laced Quantum Connections Generalising KZ

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...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 368; no. 1; pp. 1 - 54
Main Author Rembado, Gabriele
Format Journal Article
LanguageEnglish
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
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Summary: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 deformations of meromorphic connections on the sphere.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03420-9