Highest weights, projective geometry, and the classical limit: I. Geometrical aspects and the classical limit
This paper starts with a new proof that highest weight vectors for semi-simple Lie group representations can be characterised by quadratic equations, and finds the automorphism group of this quadratic variety. The idea is illustrated by various geometrical examples. Various generalisations to Cliffo...
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| Published in: | Journal of geometry and physics Vol. 34; no. 1; pp. 1 - 28 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
01.05.2000
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| ISSN: | 0393-0440, 1879-1662 |
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| Abstract | This paper starts with a new proof that highest weight vectors for semi-simple Lie group representations can be characterised by quadratic equations, and finds the automorphism group of this quadratic variety. The idea is illustrated by various geometrical examples. Various generalisations to Clifford algebras and quantum groups are explored, as well as the relationship between geometry, second quantisation, and the classical limit. |
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| AbstractList | This paper starts with a new proof that highest weight vectors for semi-simple Lie group representations can be characterised by quadratic equations, and finds the automorphism group of this quadratic variety. The idea is illustrated by various geometrical examples. Various generalisations to Clifford algebras and quantum groups are explored, as well as the relationship between geometry, second quantisation, and the classical limit. |
| Author | Hannabuss, K.C. |
| Author_xml | – sequence: 1 givenname: K.C. surname: Hannabuss fullname: Hannabuss, K.C. email: kch@ermine.ox.ac.uk organization: Balliol College, Oxford OX1 3BJ, UK |
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| Keywords | 51A50 Lie groups and Lie algebras 58F06 Classical limit Highest weight Flag manifold Pure spinor 81S10 15A66 81R50 Moment map Quantum field theory Projective geometry 22E46 |
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| SubjectTerms | Classical limit Flag manifold Highest weight Moment map Projective geometry Pure spinor |
| Title | Highest weights, projective geometry, and the classical limit: I. Geometrical aspects and the classical limit |
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