Journal of Lie Theory

no. 2
Annihilators of Simple Integrable Weight sl(∞)-Modules
Journal of Lie Theory, Volume 29 (2019) no. 2, pp. 303-310
Let g = sl(∞). We compute the annihilators of a class of simple integrable weight g-modules with finite-dimensional weight spaces. It is a claim of I. Dimitrov, that this class exhausts all simple integrable weight g-modules with finite-dimensional weight spaces. The main feature of interest is that Dimitrov's modules contains non highest weight modules. Here we provide another construction for these modules, which allows to apply recent results of A. Petukhov and I. Penkov to compute such annihilators.
DOI: 10.5802/jolt.1060
Classification: 17B65, 17B10
Keywords: Annihilator of modules, weight modules, direct limit Lie algebras 
@article{JOLT_2019_29_2_a0,
     author = {L. Calixto},
     title = {Annihilators of {Simple} {Integrable} {Weight} {sl(\ensuremath{\infty})-Modules}},
     journal = {Journal of Lie Theory},
     pages = {303--310},
     year = {2019},
     volume = {29},
     number = {2},
     doi = {10.5802/jolt.1060},
     zbl = {1439.17025},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1060/}
}
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L. Calixto. Annihilators of Simple Integrable Weight sl(∞)-Modules. Journal of Lie Theory, Volume 29 (2019) no. 2, pp. 303-310. doi: 10.5802/jolt.1060

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