Harish-Chandra modules for Yangians

V. Futorny, A. Molev and S. Ovsienko

Abstract

We study Harish-Chandra representations of the Yangian Y(gl(2)) which admit a decomposition with respect to a natural maximal commutative subalgebra Gamma and satisfy a polynomial condition. We prove an analogue of Kostant theorem showing that the restricted Yangian Y_p(gl(2)) is a free module over Gamma and show that every character of Gamma defines a finite number of irreducible Harish-Chandra modules. We study the categories of generic Harish-Chandra modules, describe their simple modules and indecomposable modules in tame blocks.