| EPSRC Reference: |
GR/R53593/01 |
| Title: |
Orientations of Coxeter matroids |
| Principal Investigator: |
Borovik, Professor A |
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| Department: |
Mathematics |
| Organisation: |
UMIST |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 August 2001 |
Ends: |
30 June 2002 |
Value (£): |
7,955
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| EPSRC Research Topic Classifications: |
| Algebra & Geometry |
Logic & Combinatorics |
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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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The theory of Coxeter matroids (which include classical matroids as a special case, for the Coxeter group An), provides a technique for the study of combinatorial aspects of the geometry and topology of flag varieties of semisimple Lie groups and Kac-Moody groups; it also simplifies and unifies classical matroid theory. The most interesting special cases correspond to Coxeter groups Cn (symplectic matroids) and Dn (orthogonal matroids).Many applications of classical matroids in topology and geometry require an extra structure, orientation. However, there are no concepts of orientation for general symplectic and orthogonal matroids. The current proposal is aimed at finding this crucial missing link of the theory. Orientation of matroids is, in the classical case, traditionally defined in terms of circuit or basis exchanges. Therefore, the theory of orientation will benefit from the introduction and detailed study of similar concepts, which is another aim of the project.We plan to apply the new technique to the construction and study of combinatorial models of flag varieties along the lines of MacPherson's construction of combinatorial Grassmannians. Another application is to the description of combinatorial invariants of the absolute Galois group action on Grothendieck's'dessins d'enfants'.
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Key Findings |
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Potential use in non-academic contexts |
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| Description |
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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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