Vol. 297, No. 1, 2018

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ISSN: 0030-8730
Non-minimality of certain irregular coherent preminimal affinizations

Adriano Moura and Fernanda Pereira

Vol. 297 (2018), No. 1, 147–193
Abstract

Let g be a finite-dimensional simple Lie algebra of type D or E and λ be a dominant integral weight whose support bounds the subdiagram of type D4. We study certain quantum affinizations of the simple g-module of highest weight λ which we term preminimal affinizations of order 2 (this is the maximal order for such λ). This class can be split in two: the coherent and the incoherent affinizations. If λ 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 λ is irregular, the coherent preminimal affinizations are not minimal under certain hypotheses. Since these hypotheses are always satisfied if g is of type D4, this completes the classification of minimal affinizations for type D4 by giving a negative answer to a conjecture of Chari and Pressley stating that the coherent and the incoherent affinizations were equivalent in type D4 (this corrects the opposite claim made by the first author in a previous publication).

Keywords
minimal affinizations, quantum affine algebras
Mathematical Subject Classification 2010
Primary: 17B10, 17B37
Secondary: 20G42
Milestones
Received: 15 January 2018
Revised: 26 June 2018
Accepted: 26 June 2018
Published: 7 October 2018
Authors
Adriano Moura
Departamento de Matemática
Universidade Estadual de Campinas
Campinas
Brazil
Fernanda Pereira
Departamento de Matemática, Divisão de Ciências Fundamentais
Instituto Tecnológico de Aeronáutica
São José dos Campos
Brazil