Details of Grant 

EPSRC Reference:	EP/H02283X/1
Title:	Unitary forms of Kac-Moody algebras and Kac-Moody groups
Principal Investigator:	Koehl, Professor R
Other Investigators:	Shpectorov, Professor S
Researcher Co-Investigators:
Project Partners:
Department:	School of Mathematics
Organisation:	University of Birmingham
Scheme:	Standard Research
Starts:	01 September 2010	Ends:	01 January 2011	Value (£):	312,191
EPSRC Research Topic Classifications:	Algebra & Geometry
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 03 Dec 2009 Mathematics Prioritisation Panel Announced
Summary on Grant Application Form
Existing cosmological theories suggest that, close to a cosmological singularity like a big-bang or a big-crunch, the description of the universe in terms of spatial continuum and space-time based quantum field theory breaks down and the information encoded in the spatial variation of the geometryof the universe gets transferred into spatially independent but time-dependent Lie-algebraic variables encoded in the infinite-dimensional symmetric space of a real split Kac-Moody algebra over its unitary form. In this context the understanding of representations of the unitary form of the real split Kac-Moody algebra of so-called type E10 is of particular interest. One such representation can be constructed as an extension to the whole unitary form of the 32-dimensional spin representation of its regular subalgebra of type A9, using a presentation by generators and relations of unitary forms given by Berman.This project is set in pure mathematics within the areas of infinite-dimensional Lie theory and geometric group theory. It will combine classical techniques from the theory of Kac-Moody algebras and Kac-Moody groups in characteristic 0 and their unitary forms with the quickly developing theory of unitary forms of Kac-Moody groups over arbitrary fields based on the theory of twin buildings. Its goal is to contribute to a uniform structure theory of unitary forms of Kac-Moody algebras and of Kac-Moody groups of indefinite type. The main emphasis of this project will be on finite-dimensional representations and on ideals and normal subgroups, respectively, of these unitary forms, starting with the above-mentioned finite-dimensional representation discovered in cosmology.
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Organisation Website:	http://www.bham.ac.uk