On a category of $g{l}_{\infty }$-modules

Abstract

We study a particular category $\mathcal{C}$ of $\gl_{\infty}$-modules and a subcategory ${\mathcal{C}}_{int}$ of integrable $\gl_{\infty}$-modules. As the main results, we classify the irreducible modules in these two categories and we show that every module in category ${\mathcal{C}}_{int}$ is semi-simple. Furthermore, we determine the decomposition of the tensor products of irreducible modules in category ${\mathcal{C}}_{int}$.

26 pages

References in corpus (1)

• W_{1+\infty} and W(gl_N) with central charge N