Minimal affinizations of representations of quantum groups: The nonsimply-laced case

Abstract

If U q (g) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representationV of U q (g) is a finite-dimensional irreducible representation\(\hat V\) of U q (ĝ) which containsV with multiplicity one, and is such that all other U q (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.