An atlas of characteristic zero representations

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/51552 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/51552 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/51552 archive 4031 disk0/00/00/14/63 2016-09-16 17:28:40 2019-01-23 09:54:14 2016-09-16 17:28:40 thesis show 0 Nickerson Simon Jon Wilson R.A. University of Birmingham An atlas of characteristic zero representations unpub QA 30sch_mats Group theory, representation, characteristic zero, semi-presentation, GAP, computational group theory, finite simple group, finite quasisimple group, sporadic group, Atlas, standard generators, rational reconstruction Hard copy thesis includes a CD-ROM, the data from which are available at http://nickerson.org.uk/atlas/ A copy of the CD-ROM is in JR's data archive folder russeljc-03 \\its-rds\archive\2015\1463_Nickerson_SJ_thesis_2006_CDROM_contents. To be transferred to published research data archive when this is available. 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and checking whether given elements of the group are standard generators. 2006-07-11 2006-01 graduation eng author This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public 231 University of Birmingham School of Mathematics d_ph org epsrc 2006-07-11 graduation