Details of Grant 

EPSRC Reference:	GR/S14900/01
Title:	Representations of Symplectic Reflection Algebras
Principal Investigator:	Gordon, Professor I
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	School of Mathematics & Statistics
Organisation:	University of Glasgow
Scheme:	First Grant Scheme Pre-FEC
Starts:	01 February 2004	Ends:	31 January 2007	Value (£):	127,912
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 29 Nov 2002 Mathematics Prioritisation Panel (Science) Deferred
Summary on Grant Application Form
Symplectic reflection algebras are intimately related to rings of differential operators, quiver varieties, Lie theory and resolutions of symplectic singularities. The representation theory of these algebras is central to the whole field, but still in its infancy. The proposed research is aimed at improving our understanding of the finite dimensional representations of symplectic reflection algebras.By results of Etingof and Ginzburg, the irreducible representations control much of the geometry associated with symplectic reflection algebras. However, even the most basic properties of the irreducible representations are unknown in general.Still more of the geometry is reflected in certain continuous families of modules, but less is known about these except in special cases.To improve our understanding of the representation theory, we will investigate the simple modules by using existing results from the theory of quiver varieties and Lie theoretic combinatorics. To make advances in the theory, we will use a number of tools, including Poisson geometry, baby Verma modules and quiver varieties.
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Organisation Website:	http://www.gla.ac.uk