Quantum algebras and symplectic reflection algebras for wreath products

To a finite subgroup Γ \Gamma of S L 2 ( C ) SL_2(\mathbb {C}) , we associate a new family of quantum algebras which are related to symplectic reflection algebras for wreath products S l ≀ Γ S_l\wr \Gamma via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reflection algebras for Γ \Gamma and construct for them a PBW basis. When Γ \Gamma is a cyclic group, we are able to give more information about their structure and to relate them to Yangians.