Abstract
Representations of the Lie algebra sl(3) with highest weight are analyzed. Invariant subspaces of indecomposable representations are determined. We study the decomposition of these representations with respect to the subalgebras su(2) and su(1,1) (in their obvious imbedding in su(2,1)).
For special cases this decomposition gives indecomposable non multiplicity free representations (indecomposable pairs) with highest weight. These were discussed in [1] and appear also in the decomposition so(3,2) ⊃ su(1,1) of the Rac representation, [7].
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References
GruberB., and KlimykA.U., J. Math. Phys. 19, 2009 (1978).
Gel'fandI.M., and GraevM.I., Izv. A.N. SSSR, Ser. Math. 29, 1329 (1965).
GruberB., and KlimykA.U., J. Math. Phys. 16, 1816 (1975).
ZelobenkoD.P., ‘Compact Lie Groups and its Representations’, Nauka, Moscow, 1970.
Gel'fandI.M., and PonomarevV.A., UMN 23, N: 23 (1968).
Indecomposable non-multiplicity free representations of su(1,1) of a different kind were found by J.M.Maillard and D.Sternheimer, C.R. Acad. Sci. Paris 280, serie A, 73 (1975) and D. Arnal and G. Pinczon, Bull. Soc. Math. France 101, 381 (1973). These representations of su(1,1) are not found in the reduction of the su(2,1) representations which are considered here.
Flato, M., and Fronsdal, C., ‘Quantum field theory of singletons. The Rac’, Preprint.
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Smirnov, Y.F., Gruber, B. Indecomposable representations of the algebra su(2,1). Lett Math Phys 4, 367–372 (1980). https://doi.org/10.1007/BF00417403
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DOI: https://doi.org/10.1007/BF00417403