Gelfand-Tsetlin modules of quantum gln defined by admissible sets of relations

The purpose of this paper is to construct new families of irreducible Gelfand-Tsetlin modules for Uq(gln). These modules have arbitrary singularity and Gelfand-Tsetlin multiplicities bounded by 2. Most previously known irreducible modules had all Gelfand-Tsetlin multiplicities bounded by 1 [16], [17]. In particular, our method provides new families of irreducible Gelfand-Tsetlin modules for gln. This generalizes the results of [10] and [15].