Finkel Morgenstern, FedericoGómez-Ullate Otaiza, DavidGonzález López, ArtemioRodríguez González, Miguel Ángel2023-06-202023-06-202001-080010-361610.1007/s002200100468https://hdl.handle.net/20.500.14352/59607©Springer. This work was partially supported by the DGES under grant PB98-0821. R. Zhdanov would like to acknowledge the financial support by the Spanish Ministry of Education and Culture during his stay at the Universidad Complutense de Madrid.A new family of AN-type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero-Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin Hamiltonians.engjournal articlehttp://dx.doi.org/10.1007/s002200100468http://link.springer.comhttp://arxiv.org/abs/hep-th/0102039open access51-73Many-body problemsAlgebraic structureIntegrable systemsGround-statePolynomialsExtensionParticlesExchangeChainFísica-Modelos matemáticosFísica matemática