NON-MINIMALITY OF CERTAIN IRREGULAR COHERENT PREMINIMAL AFFINIZATIONS

Let g be a finite-dimensional simple Lie algebra of type D or E and lambda be a dominant integral weight whose support bounds the subdiagram of type D-4. We study certain quantum affinizations of the simple g-module of highest weight lambda which we term preminimal affinizations of order 2 (this is the maximal order for such lambda). This class can be split in two: the coherent and the incoherent affinizations. If lambda is regular, Chari and Pressley proved that the associated minimal affinizations belong to one of the three equivalent classes of coherent preminimal affinizations. In this paper we show that, if lambda is irregular, the coherent preminimal affinizations are not minimal under certain hypotheses. Since these hypotheses are always satisfied if g is of type D-4, this completes the classification of minimal affinizations for type D-4 by giving a negative answer to a conjecture of Chari and Pressley stating that the coherent and the incoherent affinizations were equivalent in type D-4 (this corrects the opposite claim made by the first author in a previous publication).