  We apply the Clebsch-Gordan and Racah coefficients to calculate the double
tensors for two equivalent d electrons. We also obtain the commutation
relations for these double tensors and choose certain quantum numbers, which
produce a subgroup. From the root vectors of the commutation relations, we
identify them with Lie algebra B2. Once we have the correct Lie algebra, it is
feasible to use the Wigner-Eckart theorem to find matrix elements for
transition states among atomic spectra or nuclear shell models.
