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The invariant form of the generators of semisimple Lie and quantum algebras in their arbitrary finite-dimensional representation

A. N. Leznov
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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.

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A. N. Leznov. 1999-04-25. The invariant form of the generators of semisimple Lie and quantum algebras in their arbitrary finite-dimensional representation. https://arxiv.org/abs/math-ph/9904021

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