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

Published: 12 June 2019| Version 1 | DOI: 10.17632/3g4w8f9vdk.1
Daniel Langr,
Tomáš Dytrych,
Jerry P. Draayer,
Kristina D. Launey,
Pavel Tvrdík


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 $N=(\eta+1)(\eta+2)/2$ degenerate eigenstates of the $\eta$th 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.



Computational Physics, Nuclear Structure, Harmonic Oscillator, Group Representation Theory