Abstract:
We discuss the limits of quantum Calogero-Sutherland (CS) system for bosonic particles and fermionic particles. The bosonic limit is realized as a projective limit of finite models, it was studied by M.Nazarov and E.Sklyanin (arXiv:1309.6464) and by A.Veselov and A.Sergeev (arXiv:1311.0853) .They presented precise construction of the family of commuting Hamiltonians in the bosonic Fock space. The crucial point of their constructions is the use of equivariant family of Heckman–Dunkl operators as a quantum L-operator for the CS system. The construction of projective type limit for CS system with fermionic particles uses the same ideology — to consider the Heckman–Dunkl operator as a quantum $L$-operator for the CS system. In this case the explicit formulas for the limits of the Dunkl operators are given by means of vertex operators. The advantage of this construction is that the answers may be interpreted both in the bosonic and in the fermionic Fock space.
|
