Harish-Chandra modules for Yangians

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