Integrable representations of the quantum affine special linear superalgebra

Yuezhu Wu; R. B. Zhang

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arXiv · 1410.3974

Integrable representations of the quantum affine special linear superalgebra

Yuezhu Wu·R. B. Zhang

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Abstract

The simple integrable modules with finite dimensional weight spaces are classified for the quantum affine special linear superalgebra $\U_q(\hat{\mathfrak{sl}}(M|N))$ at generic $q$. Any such module is shown to be a highest weight or lowest weight module with respect to one of the two natural triangular decompositions of the quantum affine superalgebra depending on whether the level of the module is zero or not. Furthermore, integrable $\U_q(\hat{\mathfrak{sl}}(M|N))$-modules at nonzero levels exist only if $M$ or $N$ is $1$.

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BibTeX RIS

Yuezhu Wu, R. B. Zhang. 2014-10-15. Integrable representations of the quantum affine special linear superalgebra. https://arxiv.org/abs/1410.3974

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