Archives

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