Classificação das afinizações minimais irregulares de tipo D

Author(s)

Fernanda de Andrade Pereira

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2014-07-04

Examining board members

Adriano Adrega de Moura; Marcos Benevenuto Jardim; Vyacheslav Futorny; Bárbara Seelig Pogorelsky; Vitor de Oliveira Ferreira

• Advisor: Adriano Adrega de Moura

Abstract

The concept of minimal affinization, introduced by Chari and Pressley, arose from the impossibility to extend, in general, a representation of the quantum group associated to a simple Lie algebra for the quantum group associated to its loop algebra, which is always possible in the classical context. A special class of minimal affinizations is that of the Kirillov-Reshetikhin modules, which are minimal affinizations of the irreducible modules with highest weight multiple of a fundamental weight. These modules are central objects in the study of integrable lattices in mechanical statistics. In the past two decades it has been intense the scientific research in the direction of understanding the minimal affinizations, not only by their potential applications in mathematical physics, but also for being a very rich theory for itself, in addition to having strong interaction with combinatorics. There exists an almost complete classification of the equivalence classes of the minimal affinizations in terms of Drinfeld polynomials due to Chari and Pressley. The classification is completed in the case where the support of the highest weight does not enclose a subdiagram of type D4, and in this case there is only one equivalence class. In the case where the support encloses a subdiagram of type D4 the situation depends essentially if support contains the trivalent node of the diagram or not. If it contains, the classification is also completed and there are three equivalence classes. Otherwise the classification is not completed. In this work we present the classification of the equivalence classes for algebras of type D. The main technique used was the combinatorial manipulation of qcharacters through mainly its description via tableaux and sometimes using the Frenkel-Mukhin algorithm (AU)

• FAPESP's process: 09/16309-5 - Classification of the irregular minimal affinizations of type D
• Grantee: Fernanda de Andrade Pereira
• Support Opportunities: Scholarships in Brazil - Doctorate