## Project Details

### Description

The classical object is the symmetric group and we want to know about its representations. Each representation is like a Lego structure: it is made up of a set of building blocks. The building blocks are the irreducible representations. Over the field of complex numbers, these irreducible representations are understood and classified, and we know precisely how to join them together to make new representations. Thus over the complex numbers, we understand all representations of the symmetric groups. But over an arbitrary field, this is no longer true. We would, however, gain substantial information if we knew about the structure of certain representations, called Specht modules.

The more general objects are the cyclotomic Hecke algebras of type G(r,1,n), of which the symmetric group algebra is a particular case. When the algebra is not semisimple, very little is known about its representations, although they appear in various representation theoretic contexts, and have been shown to have deep links with algebraic Lie theory. The principal aim of this research is to investigate the properties of certain representations of the cyclotomic Hecke algebras. We would like to build on our knowledge of the symmetric group algebras to find information about these representations, but we also want to develop more general results that will take us in new directions.

Status | Finished |
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Effective start/end date | 13/09/10 → 12/12/12 |

### Funding

- Engineering and Physical Sciences Research Council: £101,514.00