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

Gabriele Rembado (1)

1 LMO - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Isomonodromic deformations; quantum integrable systems; quiver varieties; deformation quantisation; quantum Hamiltonian reduction

Domaines: Géométrie algébrique [math.AG]; Géométrie différentielle [math.DG]; Théorie des groupes [math.GR]; Topologie géométrique [math.GT]; Physique mathématique [math-ph]; Algèbres quantiques [math.QA]; Anneaux et algèbres [math.RA]; Géométrie symplectique [math.SG]

Gabriele Rembado. Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties. Symmetry, Integrability and Geometry : Methods and Applications, 2020, 16, pp.103. ⟨10.3842/SIGMA.2020.103⟩. ⟨hal-03748595⟩