On Projective Modules in Category \mathcal{O}_{int} of Quantum \mathfrak{sl}_{2} |
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Authors: | Yiqiang Li |
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Institution: | 1. Department of Mathematics, University at Buffalo, State University of New York, 244 Mathematics Building, Buffalo, New York, 14260, USA
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Abstract: | The restriction of a Verma module of ${\bf U}(\mathfrak{sl}_3)$ to ${\bf U}(\mathfrak{sl}_2)$ is isomorphic to a Verma module tensoring with all the finite dimensional simple modules of ${\bf U}(\mathfrak{sl}_2)$ . The canonical basis of the Verma module is compatible with such a decomposition. An explicit decomposition of the tensor product of the Verma module of highest weight 0 with a finite dimensional simple module into indecomposable projective modules in the category $\mathcal O_{\rm{int}}$ of quantum $\mathfrak{sl}_2$ is given. |
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