Abstract: Casimir operators for orthogonal groups are defined. Rank for semisimple groups is defined and shown to equal m for SO(2m) and SO(2m+1). It is shown that there are m independent Casimirs and a set of them is presented in the form of polynomials in the generators of degree 2k, 1 ≤ k≤ m. For SO(2m) the Casimir of degree 2m must be replaced in the integrity basis by a Casimir of degree m defined using the invariant ε tensor. This special Casimir plays a crucial role in distinguishing conjugate representations that are inequivalent. Biographical notes on Pfaff are given.
Publication Year: 2012
Publication Date: 2012-10-11
Language: en
Type: book-chapter
Indexed In: ['crossref']
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