REPSN - A GAP4 Package

Author: Vahid Dabbaghian
Needs: GAP in version at least 4.3.; GAPDoc in version at least 0.9999 for accessing the documentation
Operating systems: Any, on which GAP is running. (For the provided kernel function the operating system needs to support dynamic loading of kernel code.)
Current version: 3.0.2 (released August 2011)
Contact: vdabbagh@sfu.ca
Download: See below for archives in several formats.

Description

REPSN is a package provided for computing matrix representations in characteristic zero of finite groups. Most of the functions in REPSN have been written according the algorithm described in the author's Ph.D thesis [2] and [1] (see [3]). For constructing representations of simple groups and their covers the algorithm described in [6] has been used (see [4] and [5]). 

REPSN is applicable for any group with a character of degree less than 100. Indeed, if the group is soluble, there is no restriction on the character degree. In practice the program is quite fast when the degree is small, but can be very slow when it is necessary to call one of the subprograms which extend irreducible representations.

Installation

Detailed installation instructions are contained in the package README file.

Online Documentation

Here is the documentation of the REPSN package in several output formats. If you have installed the package as described above you can also access all of these documents from the GAP online help.

• html-version
• pdf-version
• dvi-version

Package Archives for Download

• PackageInfo.g file
• README file

The REPSN package is availabe in several formats:

• repsn3r0p2.zoo (use the "unzoo" or "unzoo.exe" from the GAP homepage)
• repsn3r0p2.tar.gz (GNU tar archive, gzip'ed)
• repsn3r0p2.tar.bz2 (GNU tar archive, bzip2'ed)
• repsn3r0p2-win.zip (with DOS/Windows style line breaks in text files)                                                                                                                                                                                                                                                                

Acknowledgements

The first version of this package was obtained during my Ph.D. studies at Carleton University. I would like to express deep gratitude to my supervisor Professor John D. Dixon whose guidance and support were crucial for the successful completion of this project. I also thank Professor Charles Wright and referees for pointing out some important comments to improve REPSN.

References

[1] Dabbaghian, V., Dixon, J. D. Computing matrix representations, Math. Comp., 79 (2010), 1801--1810.

[2] Dabbaghian-Abdoly, V. An algorithm to construct representations of finite groups, Ph.D. thesis, Dept. Mathematics, Univ. Carleton, (2003)

[3] Dabbaghian-Abdoly, V. An algorithm for constructing representations of finite groups, J. Symbolic Comput., 39 (2005), 671-- 688.

[4] Dabbaghian-Abdoly, V. Constructing representations of finite simple groups and central covers, Canad. J. Math., 58 (2006), p. 23 -- 38

[5] Dabbaghian-Abdoly, V. Constructing representations of higher degrees of finite simple groups and covers, Math. Comp., 76 (2007), p. 1661 -- 166

[6] Dixon, J. D. Constructing representations of finite groups in , Groups and Computation, Dimacs Series in Discrete Mathematics and Theoretical Computer Science, 11 (1993), p. 105 -- 112