| EPSRC Reference: |
GR/L36970/01 |
| Title: |
CAPELLI IDENTITIES FOR CLASSICAL LIE ALGEBRAS |
| Principal Investigator: |
Nazarov, Professor M |
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| Department: |
Mathematics |
| Organisation: |
University of York |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
11 February 1997 |
Ends: |
10 February 2000 |
Value (£): |
5,575
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Summary on Grant Application Form |
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The Capelli identity (1890) is one of the most famous results in classical invariant theory. It was used as a major instrument by H. Weyl in his book Classical Groups and discussed by R. Howe from the viewpoint of the modern theory of reductive dual pairs. It gives explicit formulas for the pre-images in the centre of the universal enveloping algebra U(glN) for the canonical generators of the ring of the glN x glN invariant differential operators on CM x CN where M is any non-negative integer.Recently a remarkable generalisation of the classical Capelli identity was found by this investigator and his colleague A. Okounkov. It gives explicit formulas for the pre-image in the centre of the universal enveloping algebra U(glN) for the canonical linear basis of the ring of the glN x glN invariant differential operators on CM x CN. So this result was called the higher Capelli identity. The aim of this project is to find higher Capelli identities for the other two classical Lie algebras soN and spN.We will construct canonical bases in the centres of the universal enveloping algebras U(soN) and U(spN.). We will then describe their images in the rings of respectively sp2m x soN and so*2M x spN invariant differential operators on CMxCN . This will require extensive computer experiments. According to the theory of dual pairs this description will provide analogues for soN and spN of the original Capelli identity.
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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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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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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.york.ac.uk |