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Gel'fand‐pattern technique applied to the physically important decomposition of *S U*(6)

### Abstract

Explicit and easily computable formulas for the *physical* quantum numbers *I* _{3}, *Y*, and *S* _{3}, and also two additional quantum numbers for all states spanning an arbitrary irreducible representation of *S U*(6) are obtained by using Gel'fand‐pattern technique. This result is accomplished by establishing a correspondence between the 3 diagonal generators + 2 ``quark‐spin'' generators, and the 5 ``canonical'' generators *H* _{1} − *H* _{5}, the eigenvalues of which are given by the Gel'fand patterns of *S U*(6) in the ordinary way. The content of the *S U*(6) representations taken as examples is displayed explicitly. The possibility of doing this suggests that Gel'fand patterns may be useful even in a nonmaximal decomposition, although the patterns are intrinsically linked to the ``canonical'' chain of decomposition: . The procedure developed in the case of *S U*(6) is generalized to the twofold nonmaximal decomposition of .

© 1974 The American Institute of Physics

Received 09 July 1973
Revised 24 September 1973
Published online 04 November 2003