Symbolic-Numeric Algorithm for Computing Orthonormal Basis of O(5) × SU(1,1) Group

We have developed a symbolic-numeric algorithm implemented in Wolfram Mathematica to compute the orthonormal non-canonical bases of symmetric irreducible representations of the O(5) × SU(1,1) and O(5) ¯ × SU(1,1) ¯ partner groups in the laboratory and intrinsic frames, respectively. The required orthonormal bases are labelled by the set of the number of bosons N, seniority λ, missing label μ denoting the maximal number of boson triplets coupled to the angular momentum L= 0, and the angular momentum (L, M) quantum numbers using the conventional representations of a five-dimensional harmonic oscillator in the laboratory and intrinsic frames. The proposed method uses a new symbolic-numeric orthonormalization procedure based on the Gram–Schmidt orthonormalization algorithm. Efficiency of the elaborated procedures and the code is shown by benchmark calculations of orthogonalization matrix O(5) and O(5) ¯ bases, and direct product with irreducible representations of SU(1,1) and SU(1,1) ¯ groups. © 2020, Springer Nature Switzerland AG.