If Uq (g) is a finite-dimensional complex simple Lie algebra, an affinization of a finite-dimensional irreducible representation V of Uq (g) is a finite-dimensional irreducible representation ^V of Uq (^g) which contains V with multiplicity one, and is such that all other Uq (g)-types in ^V have highest weights strictly smaller than that of V. We define a natural partial ordering ≼ on the set of affinizations of V. If g is of rank 2, we show that there is a unique minimal element with respect to this order and give its Uq (g) -module structure when g is of type _A_2 or _C_2.
Cite this article
Vyjayanthi Chari, Minimal Affinizations of Representations of Quantum Groups: the Rank 2 Case. Publ. Res. Inst. Math. Sci. 31 (1995), no. 5, pp. 873–911DOI 10.2977/PRIMS/1195163722