Weyl Modules and Frobenius-Schur Duality

• Grant number: 19/23380-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2020
• End date: February 28, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Adriano Adrega de Moura
• Grantee: Maico Gouveia de Oliveira Freitas
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/23690-6 - Structures, representations, and applications of algebraic sistems, AP.TEM

Abstract

The main goal is to provide the student with a solid background on Lie Theory, specially on finite-dimensional representations of affine Kac-Moody algebras, their quantum groups, and related algebras. The study of these topics will be motivated by the search of a solution of the following concrete problem: obtain a version of Frobenius-Schur duality which establishes an equivalence between the category of finite-dimensional modules for the affine symmetric group and a certain subcategory of that of finite-dimensional modules for an affine Kac-Moody algebra of type A also providing an explicit description of the modules for the affine symmetric which correspond to the simple and Wyl modules for the Kac-Moody algebra.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

FREITAS, Maico Gouveia de Oliveira. Dualidade afim de Schur-Weyl e módulos de Weyl. 2022. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.