Geodesic
Cyclic modules for a~complex semisimple Lie group
Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 497-510

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We consider cyclic modules generated by elementary representations of a complex semisimple Lie group. The main result is a theorem on cyclicity (Theorem 3 of § 4), according to which the elementary representations are generated by cyclic vectors of a special type with respect to a maximal compact subgroup. We give a classification of completely irreducible representations in terms of the characteristic (highest and lowest) weights. 
@article{IM2_1973_7_3_a1,
     author = {D. P. Zhelobenko},
     title = {Cyclic modules for a~complex semisimple {Lie} group},
     journal = {Izvestiya. Mathematics },
     pages = {497--510},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a1/}
}
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D. P. Zhelobenko. Cyclic modules for a~complex semisimple Lie group. Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 497-510. http://geodesic.mathdoc.fr/item/IM2_1973_7_3_a1/