\(\alpha\)-stratified modules over the Lie algebra \(sl(n,\mathbb{C})\) (Q1343436)

The article deals with the investigation of generalized Verma modules generated by an \(\alpha\)-primitive element over \(\text{sl} (n, \mathbb{C})\), which were introduced in [\textit{V. M. Futornyj} Ukr. Mat. Zh. 38, 492-497 (1986; Zbl 0614.17005)]. For these modules, a group with properties similar to the Weyl group associated with the classical Verma modules is constructed, by which a criterion of irreducibility is established and an analog of the BGG resolution is constructed.