Two programs to perform certain symbolic calculations in the enveloping algebra of a Lie algebra. The purpose of the first program (POLRANGE) is to transform a polynomial in the generators of a Lie algebra and with numerical coefficients into an equivalent form which exhibits a freely chosen but prescribed order of the generators. The purpose of the second one (ORDINVAR) is to find explicit expressions (in standard order) for the invariants of a Lie algebra, i.e. for the polynomials in the generators which commute with all generators. An appropriate choice for the Lie algebra basis and for the order of the generators in standard form, leads to algebraic closed formulae for the eigenvalues of the generalized Casimir operators upon highest weight states of irreducible representations.
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References in zbMATH (referenced in 1 article )
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- De Meyer, Hans; Vanden Berghe, G.; De Wilde, P.: Two programs to perform certain symbolic calculations in the enveloping algebra of a Lie algebra (1987)