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arXiv · 1704.01209

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

Vyacheslav Futorny·Dimitar Grantcharov·Luis Enrique Ramirez
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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 \cite{FGR2}. In particular, we show that the modules constructed in \cite{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(gl_n) and define a functor from the category of non-critical Gelfand-Tsetlin modules to the Drinfeld category.

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Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez. 2017-04-04. Drinfeld category and the classification of singular Gelfand-Tsetlin gl_n-modules. https://arxiv.org/abs/1704.01209

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