The invariant form of the generators of semisimple Lie and quantum algebras in their arbitrary finite-dimensional representation
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 Nl× Nl matrices, where Nl is the dimension of the corresponding representation, determined by the invariant Weyl formula.
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