Unitary-group canonical states and matrix elements

Abstract

States of unitary groups are realized as multinomials in boson operators, symmetrized to give symmetric-group basis states. From these, matrix elements of the group generators are calculated using the procedures discussed here. A table of basis states and matrix elements of unitary-group representations, and the values of the invariants so generated, is given for SU(1) through SU(4), for all symmetric groups from S(1) through S(3).