Drinfeld category and the classification of singular Gelfand–Tsetlin gln-modules.

We prove a uniqueness theorem for irreducible non-critical Gelfand–Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand–Tsetlin modules with 1-singularity. An explicit construction of such modules was given in Futorny et al. [ 7 ]. In particular, we show that the modules constructed in Futorny et al. [ 7 ] exhaust all irreducible Gelfand–Tsetlin modules with 1-singularity. To prove the result, we introduce a new category of modules (called Drinfeld category) related to the Drinfeld generators of the Yangian Y(gln) and define a functor from the category of non-critical Gelfand–Tsetlin modules to the Drinfeld category. [ABSTRACT FROM AUTHOR]