Efficient algorithm for representations of U(3) in U(N)

Daniel Langr, Czech Technical University in Prague
Tomáš Dytrych, Nuclear Physics Institute of the Academy of Sciences of the Czech Republic v. v. i.
Jerry P. Draayer, Louisiana State University
Kristina D. Launey, Louisiana State University
Pavel Tvrdík, Czech Technical University in Prague


An efficient algorithm for enumerating representations of U(3) that occur in a representation of the unitary group U(N) is introduced. The algorithm is applicable to U(N) representations associated with a system of identical fermions (protons, neutrons, electrons, etc.) distributed among the N=(η+1)(η+2)∕2 degenerate eigenstates of the ηth level of the three-dimensional harmonic oscillator. A C++ implementation of the algorithm is provided and its performance is evaluated. The implementation can employ OpenMP threading for use in parallel applications. Program summary: Program Title: UNtoU3.h Program files doi: http://dx.doi.org/10.17632/3g4w8f9vdk.1 Licensing provisions: MIT Programming language: C++ Nature of problem: The determination of the complete set of U(3) irreducible representations (irreps) that occurs in a representation of U(N), where N=(η+1)(η+2)∕2 is the degeneracy of the ηth harmonic oscillator shell. Solution method: The resulting set of U(3) irreps is determined by applying a simple difference relation to the U(3) weight distribution of the Gelfand basis states spanning a given U(N) irrep.