Verma modules for finite W-algebras
Lead Research Organisation:
University of Birmingham
Department Name: School of Mathematics
Abstract
The ultimate aim of this project is to determine the finite dimensional simple modules for finite W-algebras. Finite W-algebras occur in the study of infinite dimensionalrepresentations of complex semisimple Lie algebras and also in mathematical physics. Further, the representation theory of finite W-algebras has connections to the representation theory of quantum groups and cyclotomic Hecke algebras. We intend to define Verma modules for finite W-algebras, which have simple heads and such that each finite dimensional simple module occurs as one of these heads.
Organisations
People |
ORCID iD |
| Simon Goodwin (Principal Investigator) |
Publications
Brundan J
(2008)
Highest Weight Theory for Finite W-Algebras
in International Mathematics Research Notices
| Description | We developed a highest weight theory for finite W-algebras. This leads to a strategy for classifying finite dimensional irreducible modules for finite W-algebras. |
| Exploitation Route | Publication in international peer reviewed journal. Presented at international conferences. |
| Sectors | Other |
| Description | The research was published in a leading international journal and has been cited many times in other research. |
| First Year Of Impact | 2008 |
| Sector | Other |