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Weight multiplicity for unitary groups
C-478 Computer Physics Communications 14 (1978) 4 1 3 - 4 2 1 © North-Holland Publishing Company
WEIGHT MULTIPLICITY FOR UNITARY GROUPS V. A M A R , U. D O Z Z I O a n d C. O L E A R I Istituto di Fisica dell'Universiti~, Parma, Italy lstituto Nazionale di Fisica Nucleate, Sezione di Milano, Italy Received 22 June 1977; in revised form 25 January 1978
PROGRAM SUMMARY
Title of programs: DAM and DEGSUN
Other peripherals used: card reader, line printer
Catalogue number: AAAK
No. of cards in combined program and test deck: 361
Computer: CDC Cyber 76; Installation: Centro di calcolo interuniversitario dell'Italia Nordorientale, Casalecchio sul Reno BOLOGNA (Italy)
Keywords: general purpose, representation, degeneracy, U(n), unitary group, Lie algebra, weight, Gel'fand triangle
Operating system: scope 2.1. Programming language used: FORTRAN IV High speed storage required: 18 100 words No of bits in a word: 60 Overlay structure: none No. of magnetic tapes required: none
Nature of the physical problem The importance of unitary symmetries in physics is well known. This program computes the multiplicity of a weight in a given irreducible representation of U(n). Method of solution Given the rank (n - 1) of U(n) the program DAM generates the program DEGSUN. This last program computes the multiplicity of the weight m in a given irreducible representation of U(n) by properties of the Gerfand triangle. Typical running time Compile time was 14,610 s, total execution time for the test runs was 320, 733 s.
WEIGHT MULTIPLICITY FOR UNITARY GROUPS V. A M A R , U. D O Z Z I O a n d C. O L E A R I Istituto di Fisica dell'Universiti~, Parma, Italy lstituto Nazionale di Fisica Nucleate, Sezione di Milano, Italy Received 22 June 1977; in revised form 25 January 1978
PROGRAM SUMMARY
Title of programs: DAM and DEGSUN
Other peripherals used: card reader, line printer
Catalogue number: AAAK
No. of cards in combined program and test deck: 361
Computer: CDC Cyber 76; Installation: Centro di calcolo interuniversitario dell'Italia Nordorientale, Casalecchio sul Reno BOLOGNA (Italy)
Keywords: general purpose, representation, degeneracy, U(n), unitary group, Lie algebra, weight, Gel'fand triangle
Operating system: scope 2.1. Programming language used: FORTRAN IV High speed storage required: 18 100 words No of bits in a word: 60 Overlay structure: none No. of magnetic tapes required: none
Nature of the physical problem The importance of unitary symmetries in physics is well known. This program computes the multiplicity of a weight in a given irreducible representation of U(n). Method of solution Given the rank (n - 1) of U(n) the program DAM generates the program DEGSUN. This last program computes the multiplicity of the weight m in a given irreducible representation of U(n) by properties of the Gerfand triangle. Typical running time Compile time was 14,610 s, total execution time for the test runs was 320, 733 s.