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

2017/04/04 by Futorny, Vyacheslav, Grantcharov, Dimitar, Ramirez, Luis Enrique · 1 citation
#17B67 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1704.01209

Abstract

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 \citeFGR2. In particular, we show that the modules constructed in \citeFGR2 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(gl_n) and define a functor from the category of non-critical Gelfand-Tsetlin modules to the Drinfeld category.

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