Applications of group theory in physics and mathematical physics, Proc. Summer Semin., Chicago 1982, Lect. Appl. Math. 21, 179-207 (1985).
[For the entire collection see Zbl 0547.00050
This is a very nicely written review on canonical commutation relations, boson algebra, Heisenberg algebra, symplectic group and their special representations, all these here unified under the concept of dual pairs of subgroups (G,G’) of a group S, where G’ is the centralizer of G in S, and vice versa. The unification of so many concepts of interest to both the mathematicians and physicists is remarkable. The physical applications include massless particles, wave equations, Maxwell and Dirac equations, singletons, and dynamical groups of quantum system (the latter not treated in this review).