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20 April 2024

» arxiv » math-ph/9904021

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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 ;
Date:	25 Apr 1999
Subject:	Mathematical Physics \| math-ph math.MP
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 $N_l imes N_l$ matrices, where $N_l$ is the dimension of the corresponding representation, determined by the invariant Weyl formula.
Source:	arXiv, math-ph/9904021
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