Characters and cohomology of modules for affine Kac-Moody algebras and generalizations

• Grant number: 09/05887-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2009
• End date: May 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Adriano Adrega de Moura
• Grantee: Tiago Rodrigues Macedo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations, AP.TEM

Abstract

The present project aims at the study of some cohomological results for non standard flag varieties of loop groups. We are specially interested in obtaining a version of Kempf's Vanishing Theorem for the flag variety corresponding to a certain natural non standard parabolic subalgebra related to the finite-dimensional representation theory of such groups. This result will be a fundamental tool for proving a conjecture on the independence of the character of the finite-dimensional Weyl modules with respect to the (algebraically closed) ground field.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BIANCHI, ANGELO; MACEDO, TIAGO; MOURA, ADRIANO. ON DEMAZURE AND LOCAL WEYL MODULES FOR AFFINE HYPERALGEBRAS. PACIFIC JOURNAL OF MATHEMATICS, v. 274, n. 2, p. 257-303, APR 2015. (11/22322-4, 09/05887-8)

Academic Publications

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

MACEDO, Tiago Rodrigues. Caracteres e cohomologia de módulos para álgebras de Kac-Moody afim e generalizações. 2013. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.