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- Title
Drinfeld category and the classification of singular Gelfand–Tsetlin gl<sub>n</sub>-modules.
- Authors
Futorny, Vyacheslav; Grantcharov, Dimitar; Ramirez, Luis Enrique
- 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 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.
- Subjects
DRINFELD modules; OPERATOR theory; LIE algebras; MAXIMAL ideals; UNIQUENESS (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2019, Vol 2019, Issue 5, p1463
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnx159