Representations of affine wreath product algebras

• Grant number: 19/03015-5
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: April 01, 2019
• End date: May 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Iryna Kashuba
• Grantee: Eduardo Monteiro Mendonça
• Supervisor: Alistair Savage
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: University of Ottawa (uOttawa), Canada
• Associated to the scholarship: 18/07628-9 - Affine wreath product algebras, BP.MS

Abstract

The goal of this project is to study the representation theory of affine wreath product algebras. These algebras appear naturally in Heisenberg categorification and generalize many important algebras (degenerate affine Hecke algebras, affine Sergeev algebras and wreath Hecke algebras). The whole class was introduced by D. Rosso and A. Savage. The second author studied both structure and representations under the condition that the trace map F in the definition of the affine wreath product algebra is even. We would like to investigate what will happened for "odd wreath product algebras". (AU)