Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties

Symmetry Integrability and Geometry-Methods and Applications

article

Gabriele Rembado¹ 

[1] Hausdorff Centre for Mathematics

关键词: isomonodromic deformations;    quantum integrable systems;    quiver varieties;    deformation quantisation;    quantum Hamiltonian reduction 2020 Mathematics Subject Classification 81R99;   

DOI  :  10.3842/SIGMA.2020.103

来源: National Academy of Science of Ukraine

【 摘 要 】

We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Harnad duality. The quantisation of the classical symmetries involves constructing the quantum Hamiltonian reduction of the representation variety of any simply-laced quiver, both in filtered and in deformation quantisation.

【 授权许可】

Unknown