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Manuscript Title: Computation of Casimir operator eigenvalues.
Authors: A.K. Bose
Program title: CASEIG
Catalogue identifier: AARX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 28(1983)271
Programming language: Fortran.
Computer: CDC CYBER 173.
Operating system: NOS/BE 1.4.
RAM: 25K words
Word size: 60
Keywords: General purpose, Nuclear physics, Theoretical methods, Lie algebras, Casimir operators, Irreducible Representations, Group symmetries, Nuclear structure, Elementary particles.
Classification: 4.2, 17.16.

Nature of problem:
The purpose of CASEIG is to compute the eigenvalues of Casimir operators of arbitrary order for unitary unimodular, orthogonal and sympletic groups.

Solution method:
CASEIG sets up an upper triangular matrix and sums the elements of pth power of the matrix. This sum is the eigenvalue of the Casimir operator of order p. Different types of classical Lie algebras differ only in the values of certain parameters appearing in the matrix. The program is based on the results of Perelomov and Popov.

CASEIG uses rational arithmetic. The integers should be in the range -[2**48 -1] to [2**48 -1]. The program is dimensioned for matrices of size <=15. This can be easily increased subject to the overflow condition.

Unusual features:
CASEIG is written in ANSI FORTRAN 77, a subset of Fortran 5 (Data statement is non-Ansi).

Running time:
Execution times depend on the type of Lie algebra, its rank and the irreducible representation. The compile time is 1.4 s. Test runs described in the paper require from 0.3 s to 1.9 s.