Transformation brackets between U(n+1) -> U(n) -> SO(n) and U(n+1) ->   SO(n+1) -> SO(n)
  We derive a general expression for the transformation brackets between the chains U(n+1) -> U(n) -> SO(n) and U(n+1) -> SO(n+1) -> SO(n). 
Elena Santopinto, Roelof Bijker and Francesco Iachello