Abstract
Vector coherent state (VCS) theory is applied to the group chain SOn+2⊇SOn×SO2. Matrix elements of SOn+2 generators in the SOn+2⊇SOn×SO2 basis are derived. A new formula for the evaluation of some isoscalar factors for SOn+2⊇SOn×SO2 with branching multiplicity is derived in the VCS framework. As a simple example, a new expression of some isoscalar factors for SO5⊇SO3×SO2, which involves only 6j coefficients and K-normalization factors, are obtained by using this formula.
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