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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 126, Number 3, Pages 370–392
DOI: https://doi.org/10.4213/tmf436 (Mi tmf436) 		 
Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation

A. N. Leznovab

a Institute for High Energy Physics
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
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DOI: https://doi.org/10.4213/tmf436
Abstract: 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.
Received: 05.10.1999
English version:
Theoretical and Mathematical Physics, 2001, Volume 126, Issue 3, Pages 307–325
DOI: https://doi.org/10.1023/A:1010363816967
Bibliographic databases:
Language: Russian
Citation: A. N. Leznov, “Invariant Form of the Generators of Semisimple Lie and Quantum Algebras in Their Arbitrary Finite-Dimensional Representation”, TMF, 126:3 (2001), 370–392; Theoret. and Math. Phys., 126:3 (2001), 307–325
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 307--325
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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