抄録
If Uq(\mathfrak{g}) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representation V of Uq(\mathfrak{g}) is a finite-dimensional irreducible representation \hat{V} of Uq(\hat{\mathfrak{g}}) which contains V with multiplicity one, and is such that all other Uq(\mathfrak{g})-types in \hat{V} have highest weights strictly smaller than that of V. We define a natural partial ordering {\preceq} on the set of affinizations of V. If \mathfrak{g} is of rank 2, we show that there is a unique minimal element with respect to this order and give its Uq(\mathfrak{g})-module structure when \mathfrak{g} is of type A2 or C2.
