Connection of quasispin method with other group-theoretical methods

6 Connection of quasispin method with other group-theoretical 

We noted in Chapter 6 that the seniority quantum number v in reduction chain (14.38) unambiguously classifies the irreducible representations of S P4i+2 group. Then one may well ask how can the earlier group-theoretical schemes include a rotation group defined by the operators of quasispin angular momentum  

It has long been believed that there are no groups of higher rank than U414.2 that might be used to classify degenerate terms in a shell of equiva- 

Bilinear combinations composed of creation and annihilation operators can be expressed in terms of triple tensors W KkK (see (15.59) and (15.61)). In this case, these tensors are generators of the Rsi+4 group, and relationship (15.64) determines the completeness condition for the generator set of this group in relation to the commutation operation. Out of this set we shall single out two subsets of operators - and Each of 

Operator 1 ), by (15.56), is proportional to the quasispin operator, and operator W 0kK by (15.59), to double tensor with an odd sum of ranks k + k. These tensors, as shown in Chapter 14, are generators of the Sp4i+2 group, and so the above selection of generator subsets corresponds to the reduction of the Rsi+4 group on the direct product of two subgroups  

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