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

الأصل · EN

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 FGR2. In particular, we show that the modules constructed in FGR2 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.