On a certain category of $\frak{gl}_{\infty}$-modules
by
Cuipo Jiang
Haisheng Li
Vol. 14 No. 1 (2019) P.55~P.86
DOI: | https://doi.org/10.21915/BIMAS.2019104 |
| 10.21915/BIMAS.2019104 |
ABSTRACT
This is a continuation of a previous study [10] on Lie algebra $\frak{gl}_{\infty}$ in the context of quantum vertex algebras.
In this paper, we study a particular category ${\cal{C}}$ of $\frak{gl}_{\infty}$-modules and a
subcategory ${\cal{C}}_{int}$ of integrable $\frak{gl}_{\infty}$-modules.
As the main results, we classify the irreducible modules in these two categories and we show that every module in category ${\cal{C}}_{int}$ is semi-simple. Furthermore, we determine the decomposition of the tensor products of irreducible modules in
category ${\cal{C}}_{int}$.
KEYWORDS
Affine Lie Algebra, Integrable Module, Generalized Verma Module, S-singular vector.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary 17B65; Secondary 17B67, 17B69
MILESTONES
Received: 2017-06-28
Revised :
Accepted: 2018-02-19
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