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Manuscript Title: Eigenstates and eigenvalues of labelling operators for O(3) bases of U(3) representations.
Authors: W. McKay, J. Patera, R.T. Sharp
Program title: EIGLAB
Catalogue identifier: ABID_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)1
Programming language: Fortran.
Computer: CDC CYBER 74.
Operating system: SCOPE 3.4.
RAM: 114K words
Word size: 60
Keywords: Nuclear physics, High energy, Atomic physics, Representation, U(3), O(3), Lie group, Eigenvalues, Eigenstates, Labelling operator, Lie algebra, General purpose.
Classification: 4.2.

Nature of problem:
Basis states of U(3) in the O(3) representation are required to describe certain atomic nuclear or multipion states, U(3) can refer to dynamical or permutation symmetries, O(3) to angular momentum or isospin. EIGLAB computes such states as eigenstates of an O(3) scalar labelling operator Q in the enveloping algebra of U(3).

Solution method:
The program calculates the matrices for L(2) and the labelling operator Q in the Gel'fand basis of an arbitrary U(3) representation and computes their eigenvalues and common eigenstates.

Running time:
Compile time was 6.7 s, total execution time for the test runs was 26.1 s. Execution time for table 2 with Q = LTL for the representation (18,9,0) was 45 s.