| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | April 16, 2008 |
| Latest Amendment Date: | April 16, 2008 |
| Award Number: | 0802511 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Tie Luo
tluo@nsf.gov (703)292-8448 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | June 15, 2008 |
| End Date: | May 31, 2012 (Estimated) |
| Total Intended Award Amount: | $164,997.00 |
| Total Awarded Amount to Date: | $164,997.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
506 S WRIGHT ST URBANA IL US 61801-3620 (217)333-2187 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
506 S WRIGHT ST URBANA IL US 61801-3620 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ALGEBRA,NUMBER THEORY,AND COM |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The PI is proposing to study questions in combinatorial representation theory which arise from problems in mathematical physics, in particular, exactly solvable two-dimensional models in statistical mechanics and conformal field theory. Representations studied inlcude finite-dimensional and integrable modules of affine Lie algebras, loop algebras, and quantum affine algebras. Questions addressed include the Feigin Loktev conjecture for fusion product, formulas for refined (generalizations of) Littlewood-Richardson coefficients, fermionic character formulas for integrable modules of affine algebras, refinements of the Feigin-Stoyanovsky construction, and semi-infinite wedge products. The combinatorial questions include identities for certain fermionic sum formulas for multiplicity coefficients of KR-modules and their generalizations. A component of the project is a representation-theoretical construction of Baxter's matrices for generalized vertex models and the associated functional equations.
Integrable models in statistical mechanics and quantum field theory arise in various contexts in physics and mathematics. Most recently, in the study of SLE, the fractional quantum Hall effect, models for entanglement in quantum mechanics and string theory. These models, which gave rise to the invention of quantum groups, have remarkable combinatorial properties and have been a fertile ground for studying properties of representations of Lie algebras and their deformations, as well as combinatorial and algebraic identities. For example the fermionic character formulas mentioned above are intimately related to fractional statistics or anyons.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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