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AbstractFor any abelian variety X with an action of a finite complex reflection group W, Etingof, Felder,Ma and Veselov constructed a family of integrable systems on T*X. When X is a product of ncopies of an eliptic curve E and W=Sn, this reproduces the usual elliptic Calogero-Mosersystem. Recently, together with Philip Argyres (Cincinnati) and Yongchao L (KIAS), we proposedthat many of these i...