Abstract
We study Harish-Chandra representations of the Yangian Y ( g l 2 ) \mathrm {Y}(\mathfrak {gl}_2) with respect to a natural maximal commutative subalgebra. We prove an analogue of the Kostant theorem showing that the restricted Yangian Y p ( g l 2 ) \mathrm {Y}_p(\mathfrak {gl}_2) is a free module over the corresponding subalgebra Γ \Gamma and show that every character of Γ \Gamma defines a finite number of irreducible Harish-Chandra modules over Y p ( g l 2 ) \mathrm {Y}_p(\mathfrak {gl}_2) . We study the categories of generic Harish-Chandra modules, describe their simple modules and indecomposable modules in tame blocks.
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