Classification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3) | Zendy

Vyacheslav Futorny | Zendy; Dimitar Grantcharov | Zendy; Luis Enrique Ramírez | Zendy

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Classification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3)

Author(s) -

Vyacheslav Futorny,

Dimitar Grantcharov,

Luis Enrique Ramírez

Publication year - 2021

Publication title -

bulletin of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.407

H-Index - 21

eISSN - 1664-3607

pISSN - 1664-3615

DOI - 10.1142/s1664360721300012

Subject(s) - simple (philosophy) , realization (probability) , mathematics , injective function , algebra over a field , simple module , pure mathematics , lie algebra , statistics , philosophy , epistemology

We provide a classification and an explicit realization of all simple Gelfand–Tsetlin modules of the complex Lie algebra [Formula: see text]. The realization of these modules, including those with infinite-dimensional weight spaces, is given via regular and derivative Gelfand–Tsetlin tableaux. Also, we show that all simple Gelfand–Tsetlin [Formula: see text]-modules can be obtained as subquotients of localized Gelfand–Tsetlin [Formula: see text]-injective modules.

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