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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Vydané v:Journal of geometry and physics Ročník 34; číslo 1; s. 1 - 28
Hlavný autor: Hannabuss, K.C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.05.2000
Predmet:
Classical limit
Flag manifold
Highest weight
Moment map
Projective geometry
Pure spinor
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
ISSN:0393-0440, 1879-1662
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Popis
Shrnutí: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(99)00002-9