| EPSRC Reference: |
EP/C511166/1 |
| Title: |
Classical Lie Groups and Quantum Affine Algebras |
| Principal Investigator: |
Nazarov, Professor M |
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| Department: |
Mathematics |
| Organisation: |
University of York |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 May 2005 |
Ends: |
31 July 2008 |
Value (£): |
137,965
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The classical Lie groups are continuous groups most frequently appearing in various branches of Mathematics. One of them is the group of all inverti linear transformations of a finite-dimensional vector space over the field of real numbers, called the general linear group. If the vector space is equipped with a non-degenerate bilinear form, symmetric or alternating, then the group of all linear transformations preserving this form is called the orthogone or the symplectic group respectively. Representation Theory is the special branch of Mathematics which investigates, in particular, how these groups appear as symmetries of other mathematical objects. It also investigates the analogues of these groups when the basic field of real numbers is replaced by a discontinuous field, such as the field of p-adic numbers that comes from Number Theory. For the two types of basic fields, continuous and not, the corresponding representation theories appear to be far from each other. The principal aim of the proposed research is to build new bridges between the two theories, hence developing both of them. To achieve this aim, we are going to use recent advances in Quantum Mechanics and Statistical Physics which led to the discovery of new mathematical objects, called quantum affine algebras. It is the technique coming from this n mathematical area, that we will be using to build our bridges.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
http://gow.epsrc.ac.uk/ViewGrant.aspx?GrantRef=EP/C511166/1 |
| Further Information: |
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| Organisation Website: |
http://www.york.ac.uk |