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) groupsTaikomosios informatikos katedraVytauto Didžiojo universiteta