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An efficient algorithm for enumerating representations of the unitary group \(\textrm{U}(3)\) that occur in a representation of the unitary group \(\textrm{U}(N)\) is introduced. The algorithm is applicable to \(\textrm{U}(N)\) representations associated with a system of nucleons distributed among the degenerate eigenstates of the selected three-dimensional harmonic oscillator level, where each eigenstate can be occupied by up to 4 particles with different combinations of spin and isospin quantum numbers. A C++ implementation of the proposed algorithm is provided, and its performance evaluation is reported.

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Efficient Algorithm for U(N) to U(3) Representation Reduction in Isospin-Adapted Nuclear Structure Calculations

  • 会议论文

  • 发表日期：

    2025年

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  • Daniel Langr,
  • Tomáš Dytrych

摘要

An efficient algorithm for enumerating representations of the unitary group \(\textrm{U}(3)\) that occur in a representation of the unitary group \(\textrm{U}(N)\) is introduced. The algorithm is applicable to \(\textrm{U}(N)\) representations associated with a system of nucleons distributed among the degenerate eigenstates of the selected three-dimensional harmonic oscillator level, where each eigenstate can be occupied by up to 4 particles with different combinations of spin and isospin quantum numbers. A C++ implementation of the proposed algorithm is provided, and its performance evaluation is reported.