Geodesic
Reduction of irreducible unitary representations of generalized Poincaré groups with respect to their subgroups
Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 2, pp. 206-220 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem of the reduction of unitary irreducible representations of the generalized Poincaré groups $\mathscr P(1,n)$ with respect to their subgroups $\mathscr P(1, n-k)$. We find the explicit form of the unitary operator that relates the canonical basis of the representation to the $\mathscr P(1, n-k)$-basis. The action of the generators in the $\mathscr P(1, n-k)$-basis is given explicitly. The case of the inhomogeneous de Sitter group is considered in detail. 
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     author = {A. G. Nikitin and W. I. Fushchych and I. I. Yurik},
     title = {Reduction of irreducible unitary representations of generalized {Poincar\'e} groups with respect to their subgroups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {206--220},
     year = {1976},
     volume = {26},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1976_26_2_a6/}
}
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A. G. Nikitin; W. I. Fushchych; I. I. Yurik. Reduction of irreducible unitary representations of generalized Poincaré groups with respect to their subgroups. Teoretičeskaâ i matematičeskaâ fizika, Tome 26 (1976) no. 2, pp. 206-220. http://geodesic.mathdoc.fr/item/TMF_1976_26_2_a6/

[1] V. I. Fuschich, TMF, 4 (1970), 360 ; V. I. Fushchich, I. Yu. Krivsky, Nucl. Phys., B7 (1968), 79 ; B14 (1969), 573 | Zbl | DOI | DOI | MR

[2] V. I. Fushchich, Lett. Nuovo Cim., 10 (1974), 163 | DOI | MR

[3] Yu. M. Shirokov, DAN SSSR, 99 (1954), 737 | Zbl

[4] A. J. Macfarlane, J. Math. Phys., 4 (1963), 490 ; R. Fong, J. Sucher, J. Math. Phys., 5 (1964), 456 | DOI | MR | Zbl | DOI | MR

[5] A. D. Donkov, V. G. Kadyshevsky, M. D. Mateev, R. M. Mir-Kasimov, Preprint JINR E2-7936, Dubna, 1974 | MR

[6] J. J. Aghassi, P. Roman, R. M. Santilli, J. Math. Phys., 11 (1970), 2297 ; L. Castell, Nuovo Cim., 49 (1967), 285 | DOI | MR | DOI | MR

[7] V. I. Fuschich, A. L. Grischenko, A. G. Nikitin, TMF, 8 (1971), 192

[8] J. E. Roberts, Commun. Math. Phys., 3 (1966), 98 | DOI | MR | Zbl

[9] K. Inönü, E. P. Wigner, Proc. N. A. S., 39 (1953), 50 | DOI | MR

[10] E. Nelson, W. F. Stinespring, Amer. J. Math., 81 (1959), 547 | DOI | MR | Zbl

[11] V. I. Fuschich, A. G. Nikitin, I. I. Yurik, Preprint Instituta matematiki, No 5, Kiev, 1975 | MR