| EPSRC Reference: |
GR/R17546/01 |
| Title: |
Canonical Bases, Reduced Expressions and Normal Forms |
| Principal Investigator: |
Marsh, Professor BR |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
University of Leicester |
| Scheme: |
Fast Stream |
| Starts: |
22 January 2001 |
Ends: |
21 September 2003 |
Value (£): |
52,708
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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A semisimple Lie algebra of finite type possesses a universal enveloping algebra, which is an infinite dimensional associative algebra with the same representation theory. It has a natural deformation, the quantized enveloping algebra, which has played a leading role in representation theory, algebraic groups, and a variety of other areas of research since its conception in the mid 1980's. The quantized enveloping algebra has a canonical basis associated to it by Kashiwara and Luszitig, and we aim to study this via the graph of communication classes of reduced expressions for the fundamental element of the corresponding Weyl group. We shall search for descriptions of this graph using the theory of automata and normal forms, looking in particular at its topological and inductive structure, and we shall describe the regions of linearity of the piecewise-linear reparametrization functions of the canonical basis corresponding to pairs of elements in this graph, since the description of these functions is essential in understanding the canonical basis. WE shall also investigate the links between the canonical basis and the semicanonical basis, recently introduced by Lusztig.We shall Corran's expertise in the area of braids and normal forms, together with the quantum group experience of Marsh, We shall also use methods developed in recent work of Marsh and Carter and Scott's study of reduced expressions.
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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.le.ac.uk |