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

Abstract The purpose of this paper is to construct new families of irreducible Gelfand–Tsetlin modules for U q ( gl n ) . 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 gl n . This generalizes the results of [10] and [15] .