Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] aatp_v1_0.gz(6 Kbytes)
Manuscript Title: Two programs to perform certain symbolic calculations in the enveloping algebra of a Lie algebra.
Authors: H. De Meyer, G. Vanden Berghe, P. De Wilde
Program title: ORDINVAR
Catalogue identifier: AATP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 44(1987)197
Programming language: Fortran.
Computer: SIEMENS 7000 SERIES.
Operating system: BS2000.
RAM: 30K words
Word size: 32
Keywords: General purpose, Lie algebras, Invariants.
Classification: 4.2.

Nature of problem:
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.

Solution method:
From the Lie algebra structure constants (assumed to be integers), the metric tensor g is established first. Then, the transpose of the minor matrix of g is calculated with integer precision. Applying the formula defining invariants and also the ranging procedure leads to corresponding polynomial forms, such that in each term the generators of the Lie algebra basis elements occur in standard order.

The same as for the program POLRANGE. Also the degree of the invariants is restricted to six.

Running time:
For 4th degree invariant of SU(3): 4 s.