MINIMAL AFFINIZATIONS OF REPRESENTATIONS OF QUANTUM GROUPS - THE NONSIMPLY-LACED CASE

If U-q(g) is a finite-dimensional complex simple Lie algebra, an affin ization of a finite-dimensional irreducible representation V of U-q(g) is a finite-dimensional irreducible representation ($) over cap V of U-q(($) over cap g) which contains V with multiplicity one, and is suc h that all other U-q(g)-types in ($) over cap V have highest weights s trictly smaller than that of V. There is a natural partial ordering le ss than or equal to on the set of affinizations, defined by Chari. In this Letter, we describe the minimal affinizations, with respect to le ss than or equal to, when g is not simply-laced.