Abstract
Transformation brackets between U(N)⊃SO(N)⊃SO(Na)⊕SO(Nb) and U(N)⊃U(Na)⊕U(Nb)⊃SO(Na)⊕SO(Nb) for symmetric U(N) irreducible representations are derived for Na, Nb⩾2 by using bispherical coordinates in N=Na+Nb dimensions and a convolution identity for generalized Laguerre polynomials. The formula derived for the transformation brackets also applies to the special cases with Na⩾2, Nb=1 and Na=1, Nb⩾2.
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