EPSRC Reference: 
EP/H02283X/1 
Title: 
Unitary forms of KacMoody algebras and KacMoody groups 
Principal Investigator: 
Koehl, Professor R 
Other Investigators: 

Researcher CoInvestigators: 

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: 

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 bigbang or a bigcrunch, the description of the universe in terms of spatial continuum and spacetime 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 timedependent Liealgebraic variables encoded in the infinitedimensional symmetric space of a real split KacMoody algebra over its unitary form. In this context the understanding of representations of the unitary form of the real split KacMoody algebra of socalled type E10 is of particular interest. One such representation can be constructed as an extension to the whole unitary form of the 32dimensional 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 infinitedimensional Lie theory and geometric group theory. It will combine classical techniques from the theory of KacMoody algebras and KacMoody groups in characteristic 0 and their unitary forms with the quickly developing theory of unitary forms of KacMoody 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 KacMoody algebras and of KacMoody groups of indefinite type. The main emphasis of this project will be on finitedimensional representations and on ideals and normal subgroups, respectively, of these unitary forms, starting with the abovementioned finitedimensional representation discovered in cosmology.

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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.bham.ac.uk 