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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

journal contribution
posted on 2023-05-16, 17:13 authored by Peter JarvisPeter Jarvis, Zhang, RB
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 General

Volume

38

Issue

14

Pagination

L219-L226

ISSN

0305-4470

Department/School

School of Natural Sciences

Publisher

IOP Publishing Ltd

Place of publication

Bristol, England

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the physical sciences

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