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Manuscript Title: The Sp(3,R) representations of an A-particle nucleus.
Authors: C.N.M. Ng, M.J. Carvalho
Program title: SPPLETH
Catalogue identifier: ADDG_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 96(1996)288
Programming language: C.
Computer: Sun Sparc 1000.
Operating system: UNIX.
RAM: 16M words
Word size: 32
Keywords: Symplectic shell model, Configuration space, Collective spaces, Irreps, Sp(3, r), U(3), Orthogonal group, Plethysm, S-functions, S-function series, Generating functions, Symmetric group, Character table, Nuclear physics, Shell model, General purpose, Algebras.
Classification: 4.2, 17.19.

Nature of problem:
Evaluation of the plethysm of the fundamental representation of the non- compact sp(3,R) algebra.

Solution method:
Problem is solved by evaluating the S-function expansion [1] M otimes {f} * C where M and C are particular S-functions series [2, 3], {f} is a single S-function (in Littlewood's notation [2]) corresponding to a partition f of A and the symbold otimes and * denote, respectively, plethysm (symmetrized product) and outer product of S-functions. Appropriately to sp(3,R), only S-functions with up to 3 parts are retained.

The main restriction is cpu time. Also, for large values of A, memory storage may become a problem. Since the S-function expansion is an infinite expansion, a weight cut-off has to be specified. Execution time increases with increasing value of A as well as with increasing value of weight cut-off. For large values of A, execution time can be reduced by giving the expected minimum weight (dictated by Pauli principle) of the S-functions in the expansion. See long write-up for details.

Unusual features:
In order to handle very large integers with infinite precision a new data type, called "astro", was introduced. This is a linked list of integers with each node of the list representing a digit of the integer. The linked-list itself is a doubly linked list, i.e. each node has a 'previous pointer' and a 'next pointer'. The linked list has also a 'header node' which contains the start pointer, the end pointer, the length of the integer (i.e. the number of digits) and its sign.

[1] M.J. Carvalho, J. Phys. A: Math. Gen. 23(1990)1909.
[2] D.E. Littlewood The Theory of Group Characters (Oxford: Clarendon) (2nd edition 1950).
[3] R.C. King, J. Phys. A: Math. Gen. 8(1975)429; M. Yang and B.G. Wybourne, J. Phys. A: Math. Gen. 19(1983)3513.