Characters of classical limits of minimal affinizations of type E6

Author(s)

Fernanda de Andrade Pereira

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2010-12-03

Examining board members

Adriano Adrega de Moura; Luiz Antonio Barrera San Martin; Vyacheslav Futorny

• Advisor: Adriano Adrega de Moura

Abstract

The concept of minimal affinization, introduced by V. Chari and A. Pressley, arose from the impossibility of extending, in general, a representation of the quantum group associated to a simple Lie algebra to the quantum group associated to its loop algebra, which is always possible on the classical context. A special class of minimal affinizations is that of Kirillov-Reshetikhin modules, which are minimal affinizations of the irreducible modules having multiples of the fundamental weights as highest weights. These modules are objects of intensive studies because of their applications in mathematical physics. One problem of particular interest involving minimal affinizations is that of describing their characters. In this work we present some formulas for the characters of minimal affinizations when the simple Lie algebra involved is of type E6. The main strategy used here was proposed by V. Chari and A. Moura by considering the classical limit of minimal affinizations. The formulas are obtained through a systematic study of certain graded modules for the corresponding current algebra given by generators and relations. The main point is to prove that these modules are isomorphic to the classical limits of the minimal affinizations when the latter are regarded as modules for the current algebra (AU)

• FAPESP's process: 07/06807-2 - Introduction to the Representation Theory of Kac-Moody Algebras
• Grantee: Fernanda de Andrade Pereira
• Support Opportunities: Scholarships in Brazil - Master