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

• Grant number: 22/15965-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 01, 2023
• End date: July 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Adriano Adrega de Moura
• Grantee: Laura Estivalez Franco da Silva
• Supervisor: Deniz Kus
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Ruhr-Universität Bochum (RUB), Germany
• Associated to the scholarship: 21/13007-0 - Excellent filtrations and combinatorial aspects of representations of affine Kac-Moody algebras, BP.DR

Abstract

The project is dedicated to investigating certain structural problems of representations of Affine Kac-Moody algebras and related algebras by exploring the theory of excellent filtrations, also knows as Demazure flags. Traditionally, results in this area 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 mathematics and mathematical-physics. Having such application in mind, the project aims to explore such combinatorial aspects and connections in a relevant manner. For the BEPE part of the project, beside further exploring the theory of lattice paths for describing multiplicities in Demazure flags utilizing recent insights obtained by the foreigner supervisor, we also plan to focus on the problem of obtaining combinatorial descriptions of higher level Demazure crystals and its connections to nonsymmetric Macdonald polynomials. (AU)