An atlas of characteristic zero representations

Nickerson, Simon Jon (2006). An atlas of characteristic zero representations. University of Birmingham. Ph.D.

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Abstract

Motivated by the World Wide Web Atlas of Finite Group Representations and the recent classification of low-dimensional representations of quasisimple groups in cross-characteristic fields by Hiss and Malle, we construct with a computer over 650 representations of finite simple groups. Explicit matrices for these representations are available on the Internet and are included on an attached CD-ROM. Our main tool is a GAP program for decomposing permutation modules. It uses reduction modulo various primes and rational reconstruction to give an acceptable performance. In addition, we define standard generators for the groups under consideration, and exhibit black box algorithms for finding standard generators and checking whether given elements of the group are standard generators.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Wilson, R.A.UNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Schools (1998 to 2008) > School of Mathematics & Statistics
School or Department: School of Mathematics
Funders: Engineering and Physical Sciences Research Council
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/1463

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