Classification of irreducible Gelfand-Tsetlin modules of sl(3)
Representation Theory
2020-01-22 v2
Abstract
We provide a classification and an explicit realization of all irreducible Gelfand-Tsetlin modules of the complex Lie algebra sl(3). The realization of these modules uses regular and derivative Gelfand-Tsetlin tableaux. In particular, we list all simple Gelfand-Tsetlin sl(3)-modules with infinite-dimensional weight spaces. Also, we express all simple Gelfand-Tsetlin sl(3)-modules as subquotionets of localized Gelfand-Tsetlin E_{21}-injective modules.
Cite
@article{arxiv.1812.07137,
title = {Classification of irreducible Gelfand-Tsetlin modules of sl(3)},
author = {Vyacheslav Futorny and Dimitar Grantcharov and Luis Enrique Ramirez},
journal= {arXiv preprint arXiv:1812.07137},
year = {2020}
}
Comments
Preliminary version. 97 pages, 46 pictures