Open AccessClassification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3)
Author(s) -
Vyacheslav Futorny,
Dimitar Grantcharov,
Luis Enrique RamĂrez
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 , pure mathematics , simple module , 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.