Sp(3,$R$) decomposition of the SU(3) no-core shell model basis*

Numerical evidence shows an important role of the symplectic Sp(3,$R$) symmetry in the ab initio no-core shell model results for light nuclei. Therefore, the construction of symplectic states from SU(3) states is necessary, as a prerequisite and crucial step of understanding the symplectic symmetry for those nuclei. This presentation will provide an introduction to our numerical calculation that decomposes the basis states of Sp(3,$R$) irreducible representations in terms of SU(3) nuclear basis. We use the null space of the Sp(3,$R$) generator $B^{(02)}$ to find the extremal states, and then ladder them with the generator $A^{(20)}$ to build the entire irreps.