Families of irreducible singular Gelfand-Tsetlin modules of gl(n)

We prove a conjecture for the irreducibility of singular Gelfand-Tsetlin modules announced in Futorny et al. (2016) [3]. Furthermore, by using the description of the irreducible subquotients for generic Gelfand-Tsetlin modules, we construct the irreducible subquotients of some classes of singular Gelfand-Tsetlin modules.