Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs

Normalized lowering and raising operators are constructed for the orthogonal group in the canonical group chain O(n) ⊃ O(n − 1) ⊃ … ⊃ O(2) with the aid of graphs which simplify their construction. By successive application of such lowering operators for O(n), O(n − 1), … on the highest weight states...

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Bibliographic Details
Published in:Journal of mathematical physics 1967-06, Vol.8 (6), p.1233-1251
Main Authors: Pang, Sing Chin, Hecht, K. T.
Format: Article
Language:English
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Summary:Normalized lowering and raising operators are constructed for the orthogonal group in the canonical group chain O(n) ⊃ O(n − 1) ⊃ … ⊃ O(2) with the aid of graphs which simplify their construction. By successive application of such lowering operators for O(n), O(n − 1), … on the highest weight states for each step of the chain, an explicit construction is given for the normalized basis vectors. To illustrate the usefulness of the construction, a derivation is given of the Gel'fand‐Zetlin matrix elements of the infinitesimal generators of O(n).
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1705340