Letters in Mathematical Physics

, Volume 30, Issue 2, pp 131–145 | Cite as

Small representations of quantum affine algebras

  • Vyjayanthi Chari
  • Andrew Pressley
Article

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 (sln+1). We call such representations ‘small’. In 1986, Jimbo defined a family of homomorphismsev a from U q (sln+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ∈ ℂ·. A second family,ev a can 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 (sln+1) byev a orev a for somea ∈ ℂ·.

Mathematics Subject Classification (1991)

17B37 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Vyjayanthi Chari
    • 1
  • Andrew Pressley
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaRiversideUSA
  2. 2.Department of MathematicsKing's CollegeLondonUK

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