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Manuscript Title: Construction of symmetric group representation matrices and states.
Authors: M.F. Soto Jr., R. Mirman
Program title: SYMSTATS
Catalogue identifier: AAME_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 23(1981)95
Programming language: PL/1.
Computer: IBM 3033.
Operating system: OS/MVT/ASP.
RAM: 216K words
Word size: 8
Peripherals: magnetic tape.
Keywords: General purpose, Algebras, Symmetric group, Irreducible Representation, Representation matrices, Basis vectors, Basis states, Basis state operators, Explicit construction.
Classification: 4.2.

Subprograms used:
Cat Id Title Reference
AAMC_v1_0 SYMGRPTB CPC 23(1981)81

Nature of problem:
To find explicitly basis states and basis state operators for the symmetric groups, in a form applicable to any symmetric group and most useful for applications.

Solution method:
The states are realized by sums of products of boson-type operators, whose indices show the permutations, concatenated with the relevant matrix elements. They are produced by direct construction.

The program can be used for any symmetric group, for which machine time and storage are available. However, for S(10) and above, there must be some modifications because the numbers then consist of two digits.

Running time:
Through S(4): 30.00 s.