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# Advances in Theoretical and Mathematical Physics

## Volume 20 (2016)

### Number 3

### Integrable representations of the quantum affine special linear superalgebra

Pages: 553 – 593

DOI: http://dx.doi.org/10.4310/ATMP.2016.v20.n3.a3

#### Authors

#### Abstract

The simple integrable modules with finite dimensional weight spaces are classified for the quantum affine special linear super-algebra $U_q (\widehat{\mathfrak{sl}} (M \vert N))$ 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 $U_q (\widehat{\mathfrak{sl}} (M \vert N))$-modules at nonzero levels exist only if $M$ or $N$ is $1$.