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Abstract: There are known to be integrable Sutherland models associated to every realroot system - or, which is almost equivalent, to every real reflection group.Real reflection groups are special cases of complex reflection groups. In thispaper we associate certain integrable Sutherland models to the classical familyof complex reflection groups. Internal degrees of freedom are introduced,defining dynamical spin chains, and the freezing limit taken to obtain staticchains of Haldane-Shastry type. By considering the relation of these models tothe usual BC N case, we are led to systems with both real and complexreflection groups as symmetries. We demonstrate their integrability by means ofnew Dunkl operators, associated to wreath products of dihedral groups.

Author: N. Crampe, C. A. S. Young


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