Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI

Abstract: We consider the isomonodromic formulation of the Calogero-Painlev\'e multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlev\'e equations. We also provide multi-particle generalizations of these integral representations.