Classification conjecture for finite-dimensional irreducible type-1 comodules of the affine quantum group

Let $\widehat{SL_q(2)}$ be the quantum group defined in the paper, and let a type $\mathbf{1}$ comodule mean a comodule whose associated $\mathcal{T}$-comodule coaction acts semisimply. For parameters $a_1,\ldots,a_n$ and spectral parameters $r_1,\ldots,r_n$, write $W_{a_i}(r_i)$ for the corresponding finite-dimensional comodules. Classification conjecture. Every finite-dimensional irreducible type $\mathbf{1}$ comodule of $\widehat{SL_q(2)}$ is isomorphic to a tensor product

$$W_{a_1}(r_1) \otimes W_{a_2}(r_2) \otimes \cdots \otimes W_{a_n}(r_n).$$

This proposes a tensor-product classification of finite-dimensional irreducible comodules of type $\mathbf{1}$; the supplied text does not state a resolution or further precise conditions on the factors.