Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs
- 1 June 1967
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 8 (6), 1233-1251
- https://doi.org/10.1063/1.1705340
Abstract
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).This publication has 13 references indexed in Scilit:
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