Title of program: FREUD Restrictions on the complexity of the problem Catalogue number: AAAA The program handles all Lie algebras of rank ~9 and repre' Program obtainablefrom: CPC Program Library, Queen's Uni-sentations With fewer than 1,000 weights. versity of Belfast, N. Ireland (see application form in this issue) Computer: IBM 370/165. Installation: Uni-Coll Corporation Typical running times Operating system: HASP-Il F 4, highest weight 0100, 0~8sec; A3, highest weight = Programming language used: FORTRAN IV 00, 0.03 sec. High speed store required: 46 807 words. No. of bits in a word: 16 Overlay structure: None No. of magnetic tapes required: none Unusual features of the program Due to the use of Weyl reflections and emphasis on domi-Otherperipherals: Card reader, line printer nant weights, this implementation is more efficient than those No. of cards in combined program and test deck: 1024 reported in [1] and [2]. By removing the I/O, the program can Card punching code: EBCDIC be used as a subroutine in the computation of outer multipli-Keywords descriptive of problem and method of solution: cities. By using the IBM 360 Fortran IV IMPLICIT statement General, Lie algebra, inner multiplicity, representation, all variables in the program are declared to be integers. When Freudenthal's formula, character. running on computers other than the IBM 360 and 370 series variables not beginning with Ito N will have to be declared as Nature of the physical problem type INTEGER. To compute the weight diagram of an irreducible representation p of a complex simple Lie algebra. This problem is equivalent to computing the character ofp. References Method of solution [1] V.K. Agrawala and J.G.F. Belinfante, Weight Diagrams The weight system ofthe representation is generated using for Lie Group Representations: A Computer Implementa-Dynkin's algorithm. Inner multiplicities of the dominant tion of Freudenthal's Algorithms in ALGOL and FORTRAN, weights are computed using Freudenthal's formula. The multi-BIT 9 (1969) 301-314. plicities of the non-dominant weights are computed recursively [2) Mark I. Krusemeyer, Determining Multiplicities of Domiusing a method, based on Weyl reflections, of fmding equiva-nant Weights in Irreducible Lie Algebra Representations lent dominant weights. Using a Computer, BIT 11(1971) 310-316.