Teoretičeskaâ i matematičeskaâ fizika, Tome 126 (2001) no. 3, pp. 370-392
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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/
@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},
year = {2001},
volume = {126},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a1/}
}
TY - JOUR
AU - A. N. Leznov
TI - Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 2001
SP - 370
EP - 392
VL - 126
IS - 3
UR - http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a1/
LA - ru
ID - TMF_2001_126_3_a1
ER -
%0 Journal Article
%A A. N. Leznov
%T Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 370-392
%V 126
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2001_126_3_a1/
%G ru
%F TMF_2001_126_3_a1
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.
