Quantum Hall fluids, Laughlin wave functions, and ideals in the Weyl algebra

It is known that non-commutative fluids used to model the Fractional Quantum Hall effect give Calogero–Moser systems. The group-theoretic description of these as reductions of free motion on type A Lie algebras leads directly to Laughlin wave functions. The Calogero–Moser models also parametrise the right ideals of the Weyl algebra, which can be regarded as labelling sources in the fluid.