On a Certain Category of $\frak{gl}_{\infty}$-modules
by
Cuipo Jiang, Haisheng Li
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
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary:
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