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Resolution of the GL(3) O(3) state labelling problem via the O(3)-invariant Bethe subalgebra of the twisted Yangain
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalizable set of Casimir operators in the subgroup chain GL(3) ⊃ O(3) ⊃ O(2). Moreover, this 'missing label' operator must be a function of the two independent cubic and quartic invariants which can be constructed in terms of the angular momentum vector and the quadrupole tensor. It is pointed out that there is a unique (in a well-defined sense) combination of these which belongs to the O(3)-invariant Bethe subalgebra of the twisted Yangian Y(GL(3); O(3)) in the enveloping algebra of GL(3). © 2005 IOP Publishing Ltd.
Funding
Australian Research Council
History
Publication title
Journal of Physics A: Mathematical and GeneralVolume
38Issue
14Pagination
L219-L226ISSN
0305-4470Department/School
School of Natural SciencesPublisher
IOP Publishing LtdPlace of publication
Bristol, EnglandRepository Status
- Restricted