Canonical solution of the SU(3) ↓ SO(3) reduction problem from the SU(3) pattern calculus |
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Authors: | Harold W Galbraith James D Louck |
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Institution: | (1) RR4, Box 726G, 13326 Cooperstown, NY, U.S.A.;(2) Theoretical Division, Los Alamos National Laboratory, 87545 Los Alamos, NM, U.S.A. |
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Abstract: | Because of its numerous applications to physics, there have been many solutions published on the problem of reducing a given irreducible representation (irrep) of the unitary unimodular group SU(3) into irreps of the proper orthogonal subgroup SO(3). Such solutions are generally based on an arbitrary construction of a nonorthogonal basis of the highest weight space for an irrep of SO(3), followed by an equally arbitrary orthonormalization procedure. This paper presents a unique solution of this problem based on the intrinsic structure of the multiplicity function, which is a function M
L(p, q) giving the number of times irrepL] of SO(3) is contained in irreppq0] of SU(3). This structure is implemented uniquely into the reduction problem through the use of the SU(3) pattern calculus.Work performed under the auspices of the U.S. Department of Energy. |
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Keywords: | 20C35 20G05 20G45 47B37 |
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