Abstract
If Uq(g) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representationV of Uq(g) is a finite-dimensional irreducible representation\(\hat V\) of Uq(ĝ) which containsV with multiplicity one, and is such that all other Uq(g)-types in\(\hat V\) have highest weights strictly smaller than that ofV. There is a natural partial ordering\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } \) on the set of affinizations, defined by Chari. In this Letter, we describe the minimal affinizations, with respect to\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \prec } \), when g is not simply-laced.
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