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

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

## Description

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.