Geodesic
Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 3, pp. 370-392

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An explicit form of the generators of quantum and ordinary semisimple algebras for an arbitrary finite-dimensional representation is found. The generators corresponding to the simple roots are obtained in terms of a solution of a system of matrix equations. The result is presented in the form of $(N_l\times N_l)$ matrices, where $N_l$ is the dimension of the corresponding representation determined by the invariant Weyl formula. 
@article{TMF_2001_126_3_a1,
     author = {A. N. Leznov},
     title = {Invariant {Form} of the {Generators} of {Semisimple} {Lie} and {Quantum} {Algebras} in {Their} {Arbitrary} {Finite-Dimensional} {Representation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {370--392},
     publisher = {mathdoc},
     volume = {126},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a1/}
}
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A. N. Leznov. Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 3, pp. 370-392. http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a1/