Simple bounded weight modules of $\displaystyle{\mathfrak{sl}(\infty)}$, $\displaystyle{\mathfrak{o}(\infty)}$, $\displaystyle{\mathfrak{sp}(\infty)}$

Dimitar Grantcharov; Ivan Penkov

Simple bounded weight modules of $\displaystyle{\mathfrak{sl}(\infty)}$, $\displaystyle{\mathfrak{o}(\infty)}$, $\displaystyle{\mathfrak{sp}(\infty)}$

Representation Theory 2018-07-06 v1

Authors: Dimitar Grantcharov , Ivan Penkov

Abstract

We classify the simple bounded weight modules of ${\mathfrak{sl}(\infty})$ , ${\mathfrak{o}(\infty)}$ and ${\mathfrak{sp}(\infty)}$ , and compute their annihilators in $U({\mathfrak{sl}(\infty}))$ , $U({\mathfrak{o}(\infty))}$ , $U({\mathfrak{sp}(\infty))}$ , respectively.

Cite

@article{arxiv.1807.01899,
  title  = {Simple bounded weight modules of $\displaystyle{\mathfrak{sl}(\infty)}$, $\displaystyle{\mathfrak{o}(\infty)}$, $\displaystyle{\mathfrak{sp}(\infty)}$},
  author = {Dimitar Grantcharov and Ivan Penkov},
  journal= {arXiv preprint arXiv:1807.01899},
  year   = {2018}
}

Comments

33 pages

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