Excellent filtrations and combinatorial aspects of representations of affine Kac-Moody algebras

• Grant number: 21/13007-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2022
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Adriano Adrega de Moura
• Grantee: Laura Estivalez Franco da Silva
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 22/15965-0 - Excellent filtrations and combinatorial aspects of representations of affine Kac-Moody algebras, BE.EP.DR

Abstract

The project is dedicated to investigating certain structural problems of representations of Affine Kac-Moody algebras e related algebras such as the description of the multiplicities of the simple factors of tensor products of two simple integrable modules and character formulas for local Weyl modules for the underlying current algebra. The main tool we plan to utilize is the theory of excellent filtrations, also knows as Demazure flags. Traditionally, answers to these type of problems have strong combinatorial flavor and connections to the theories of partitions and MacDonald polynomials which, in their turn have several applications in other areas of Matehmatics and Mathematical-Physics. Having such application in mind, the project aims to explore such combinatorial aspects and connections in a relevant manner. (AU)