  We address the removal of states with center-of-mass excitation from the
SU(3) no-core shell model [SU(3)-NCSM] space, i.e., construction of the
nonspurious subspace. A procedure is formulated based on solution of the
null-space problem for the center-of-mass harmonic oscillator lowering operator
Bcm, operating at the level of SU(3) irreducible representations. Isolation of
the center-of-mass free subspace for the SU(3)-NCSM provides the foundation for
exact removal of center-of-mass dynamics in the proposed Sp(3,R) symplectic
no-core shell model. We outline the construction process for the matrix
representation of Bcm, present the algorithm for obtaining the nonspurious
space, and examine the dimensions obtained for center-of-mass free SU(3)
subspaces in representative light nuclei.
