Inner multiplicity of unitary groups — A modified version

✍ Scribed by Samuel Thomas

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 343 KB
• Volume: 44
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(87)90029-4

✦ Synopsis

Title of program: IMUG1 counting all distinct Gelfand patterns which belong to the same weight [1]. Catalogue number: AATL Restriction on the complexity of the problem Program obtainable from: CPC Program Library, Queen's Urn-The program as implemented here can handle SU(n) groups versity of Belfast, N. Ireland (see application form in this with a rank less than or equal to 29. issue) Typical running time Computer: Honeywell DPS 8 or Any IBM PC Compatible

The multiplicity y(O, 0, 0, 0, 0) 5 in the representation Micro; Installation: Royal Military College, Kingston D(1, 1, 0, -1, -1) is calculated in 0.31 s by the Honeywell computer and in 20 s by the microcomputer. The multiplicity Operating system: Honeywell-CP6, Micro-MSDOS ver2.1 y(O, 0, 0, 0, 0, 0, 0, 0, 0, 0) = 90 in the representation D(1, 1, 1,1,0,0, -1, -1, -1, -1) is calculated in 1.6sby the Programming language used: FORTRAN 77

Honeywell computer and 295 s by the microcomputer. As expected if the multiplicity is a large number it takes more time No. of bits in a word: 36 for Honeywell, 16 for Micro to calculate it. The third example for n 30 given below took 0.5 s by the mainframe computer and 75 s by the micro. Peripherals used: disk (hard and floppy) and terminal

Unusual features of the program No. of lines in combined program and test deck: 470

There is no restriction on the dimension of the representation.

Other programs [2] have restriction on the dimension of the Keywords: general purpose, Lie algebra, inner multiplicity, representation. This program can be easily modified for higher unitary groups, Gelfand patterns rank algebras by adding and modifying certain source statements which are marked by comment lines. This program can Nature of the problem also be used to obtain the various possible Gelfand patterns To compute the inner multiplicity of a particular weight in a from a given partition. given representation for the special unitary groups using Gelfand patterns.