# EP/G04984X/1 - Representation theory of complex reflection groups and related objects

Research Perspectives grant details from EPSRC portfolio

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Research Perspectives grant details from EPSRC portfolio

Principal Investigator - Sch of Mathematics, University of Edinburgh

Start Date

09/2009

End Date

08/2012

Value

£204,582

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Summary and Description of the grant

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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Name: Representation theory of complex reflection groups and related objects - EP/G04984X/1

Start Date: 2009-09-01T00:00:00+00:00

End Date: 2012-08-31T00:00:00+00:00

Organization: University of Edinburgh

Description: 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 ...