ИСТИНА

The classical Calogero-Moser problems are known to have several quantum integrable versions, which are non-symmetric (so-called deformed quantum Calogero-Moser systems). The importance of the deformed Calogero-Moser systems became clear after the discovery of their deep relations with the theory of generalised discriminants, with the theory of simple Lie superalgebras as well as of an intriguing link with the theory of logarithmic Frobenius structures. Their integrability is not obvious at all and initially was proved by lengthy calculations. I will explain how the integrability of the deformed Calogero-Moser systems can be easily "seen from infinity" by developing the corresponding Dunkl operator technique for the infinite number of particles. As a corollary a quantum Lax matrix and a simple construction of the integrals for the deformed Calogero-Moser systems will be presented. The talk is based on the recent paper with A.N. Sergeev