Linear and unitary representations of posets: subspaces, a quadratic form, and induced modules

• Grant number: 17/24563-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 10, 2018
• End date: June 06, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Kostiantyn Iusenko
• Grantee: Kostiantyn Iusenko
• Visiting researcher: Mark Kleiner
• Visiting researcher institution: Syracuse University, United States
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

This is a research project in the area of representation theory of posets. The following problems will be studies: categorical connection between linear and unitary representations of posets, dimensions of indecomposables and quadratic forms associated with posets, explicit formulas in the language of induced modules for the Coxeter functors. (AU)