Abstract
We characterize the finite-dimensional representations of the quantum affine algebra U q (\(\widehat{sl}\) n+1) (whereq ∈ ℂ× is not a root of unity) which are irreducible as representations of U q (sl n+1). We call such representations ‘small’. In 1986, Jimbo defined a family of homomorphismsev a from U q (sl n+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ∈ ℂ·. A second family,ev acan be obtained by a small modification of Jimbo's formulas. We show that every small representation of U q (\(\widehat{sl}\) n+1) is obtained by pulling back an irreducible representation of U q (sl n+1) byev a orev afor somea ∈ ℂ·.
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Chari, V., Pressley, A. Small representations of quantum affine algebras. Lett Math Phys 30, 131–145 (1994). https://doi.org/10.1007/BF00939701
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DOI: https://doi.org/10.1007/BF00939701