Details of Grant 

EPSRC Reference:	EP/G04984X/1
Title:	Representation theory of complex reflection groups and related objects
Principal Investigator:	Chlouveraki, Dr M
Other Investigators:
Researcher Co-Investigators:
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Department:	Sch of Mathematics
Organisation:	University of Edinburgh
Scheme:	Postdoc Research Fellowship
Starts:	01 September 2009	Ends:	31 August 2012	Value (£):	204,582
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 17 Mar 2009 Maths Postdoctoral Fellowships Interview Panel Announced 12 Feb 2009 Maths Postdoctoral Research Fellowships 2008/2009 Excluded
Summary on Grant Application Form
The finite groups of matrices with rational coefficients generated by reflections, known as Weyl groups, are a fundamental building block in the classification of simple complex Lie groups as well as simple algebraic groups. They are also a foundation for many other significant mathematical theories including braid groups and Hecke algebras.The Weyl groups are particular cases of complex reflection groups, finite groups of matrices with complex coefficients generated by pseudo-reflections (elements whose vector space of fixed points is a hyperplane). Through recent work on representations of reductive groups over finite fields based upon George Lusztig's fundamental work, and motivatedby conjectures about modular representations of general finite groups, it has become clearer and clearer that the complex reflection groups behave very much like Weyl groups, and might even be as important. For example, convincing indices tend to show that, although complex reflection groups which are not Weyl groups do not define finite groups over finite fields, they might be associated to similar mysterious objects, the Spetses .The aim of my work is to find a unifying mathematical theory for the study of complex reflection groups. This theory will be used to answer important questions about the representation theory of structures associated to complex reflection groups, such as Hecke algebras and Cherednik algebras, and will lead us towards the discovery of Spetses.
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