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

Abstract

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.

Reference to arXiv:1309.1716 added

References in corpus (2)

• The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
• Symmetries of quantum Lax equations for the Painlevé equations

Cited by in corpus (1)

• $\mathrm{Sp}(1)$-symmetric hyperkähler quantisation