  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.
