Geodesic
On boson representation of angular momentum. II
Teoretičeskaâ i matematičeskaâ fizika, Tome 18 (1974) no. 3, pp. 342-352 Cet article a éte moissonné depuis la source Math-Net.Ru

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The states of a system of $N$ harmonic oscillators with fixed total number of quanta are decomposed with respect to bases of irreducible representations of $SU(2)$. The previously introduced basis [1] is a basis with the highest dimensionality in this decomposition. For the case of three harmonic oscillators, the operators and a discrete basis of a representation of the noncompact group $SU(1,1)$ are constructed. Bargmann's representation is considered for these states. 
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     author = {V. V. Mikhailov},
     title = {On~boson representation of angular {momentum.~II}},
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V. V. Mikhailov. On boson representation of angular momentum. II. Teoretičeskaâ i matematičeskaâ fizika, Tome 18 (1974) no. 3, pp. 342-352. http://geodesic.mathdoc.fr/item/TMF_1974_18_3_a5/

[1] V. V. Mikhailov, TMF, 15 (1973), 367

[2] I. M. Gelfand, R. A. Minlos, Z. Ya. Shapiro, Predstavleniya gruppy vraschenii i gruppy Lorentsa, Fizmatgiz, 1958

[3] G. Polia, Amer. Math. Monthly, 63 (1956), 689 | DOI | MR

[4] V. V. Mikhailov, Phys. Lett., 40A (1972), 343 | DOI

[5] J. Schwinger, Quantum Theory of Angular Momentum, eds. L. C. Biedenharn, H. Van Dam, Academic Press, N. Y., 1965 | MR

[6] A. O. Barut, Lectures in theoretical physics, vol. 9A, Gordon and Breach, 1967 | MR

[7] V. Bargmann, Rev. Mod. Phys., 34 (1962), 829 | DOI | MR | Zbl