2019 / March Volume 14 No.1
On a certain category of $\frak{gl}_{\infty}$-modules
Published Date |
2019 / March
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Title | On a certain category of $\frak{gl}_{\infty}$-modules |
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Pagination | 55-86 |
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 ${\cal{C}}_{int}$.
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DOI | |
AMS Subject Classification |
Primary 17B65; Secondary 17B67, 17B69
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Received |
2017-06-28
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Accepted |
2018-02-19
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