Verma-type modules for quantum affine Lie algebras (Q1780988)

In the paper under review the authors construct quantum deformations of Verma-type modules over untwisted affine Kac-Moody algebras. It is shown that the deformation the authors provide preserves the weight structure of a module. The authors prove a general irreducibility criterion for quantum Verma-type modules and investigate the structure of quantum imaginary Verma modules at level zero (when they are reducible). The obtained results show a close similarity to the classical results from [\textit{V. M. Futorny}, Can. Math. Bull. 37, No. 2, 213--218 (1994; Zbl 0829.17017)].