  Classical Calogero-Moser models with rational potential are known to be
superintegrable. That is, on top of the r involutive conserved quantities
necessary for the integrability of a system with r degrees of freedom, they
possess an additional set of r-1 algebraically and functionally independent
globally defined conserved quantities. At the quantum level, Kuznetsov
uncovered the existence of a quadratic algebra structure as an underlying key
for superintegrability for the models based on A type root systems. Here we
demonstrate in a universal way the quadratic algebra structure for quantum
rational Calogero-Moser models based on any root systems.
