| EPSRC Reference: |
GR/M22536/01 |
| Title: |
ALGEBRAS ARISING IN LIE THEORY AND PHYSICS: REPRESENT- ATION THEORY & APPLICATIONS TO STATISTICAL MECHANICS |
| Principal Investigator: |
Martin, Professor PP |
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| Department: |
Mathematics |
| Organisation: |
City, University of London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 1999 |
Ends: |
30 September 2002 |
Value (£): |
116,094
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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We propose to determine the spectrum multiplicities for various quantum spin chain Hamiltonians of physical interest using algebraic tools, particularly techniques from algebraic Lie theory. We propose further to physically characterise and compute the spectra of these Hamiltonians using a fully algebraic implementation of the Bethe ansatz. We will interpret these results from the point of view of critical phenomena in various many body problems in solid state physics and particle theory, as modelled in lattice statistical mechanics.We propose to develop and extend the applicability of aspects of Kazhdan-Lusztig theory, in particular Soergels recent determination of the characters of tilting modules for quantum groups, to transfer matrix algebras. Of specific interest are Hecke algebra quotients such as those in Schur-Weyl duality to Lie super-algebras. We will develop a formalism for analysing towers of algebras exhibiting quasi-heredity, localisation and analogues of Jantzens translation functors. We will give an interpretation of Kazhdan-Lusztig polynomials in transfer matrix algebra structure theory. This would parallel the situation for e.g. Category modules in the radical filtrations of Verma modules.
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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: |
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| Further Information: |
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| Organisation Website: |
http://www.city.ac.uk |