On representations of quantum and classical Kac-Moody algebras

• Grant number: 06/00833-9
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2006
• End date: May 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Adriano Adrega de Moura
• Grantee: Adriano Adrega de Moura
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project is concerned with 2 directions of the Representation Theory of classical and quantum Kac-Moody Algebras, which are of great present interest in various areas of Mathematics and Physics.The first one is on finite-dimensional representations of the Affine Algebras, where we focus in the theory of q-caracters and the structure theory of the Kirillov-Reshetikhin modules, both in the classical, quantum, and root of unity setting.The second focuses on finding some "canonical" bases for certain non-integrable representations, with spetial atention to the algebraic-geometry point of view of the theory as, for instance, its development from quiver varieties. (AU)