Gelfand--Tsetlin bases for representations of ${\mathrm{U}}_q({\mathfrak{g}\mathfrak{l}}_n)$ at roots of unity

In this paper, we construct Gelfand–Tsetlin bases for representations of ${\mathrm{U}}_q({\mathfrak{g}\mathfrak{l}}_n)$ at roots of unity. As an application, we obtain explicit bases for certain baby Verma modules of ${\mathrm{U}}_q({\mathfrak{g}\mathfrak{l}}_3)$ and determine their composition series.