An Atlas of sporadic group representations

Summary

Abstract

We describe a collection of several hundred representations of 25 of the 26 sporadic groups, and many related groups. All these representations are available on the world-wide web.

Introduction

The ‘atlas of finite groups’ [5] was originally conceived by its authors as Volume 1 of a series, as its subtitle ‘Maximal subgroups and ordinary characters for simple groups’ might suggest. In the event, subsequent volumes have been rather slow to appear, with Volume 2, the ‘sc Atlas of Brauer characters’ (or ‘ABC’ for short [8]), being published in 1995, just in time for this conference. Indeed, even this is only Part 1 of Volume 2, as the accidentally undeleted subtitle on page 1 proclaims, in that it only includes groups of order up to 10⁹.

At this conference, several suggestions for Volume 3 have been made, most involving large quantities of data stored on computers. It seems likely that whatever Volume 3 eventually turns out to be, it will not be a big heavy book of the type hitherto associated with the word ‘atlas’.

My own submission as a candidate for Volume 3 is a collection of explicit representations of groups. A number of these were mentioned in the ‘atlas of finite groups’ under the now notorious phrase ‘Explicit matrices have been computed.’ Many others have been computed since. In fact, it is difficult to know where to stop with such a collection of representations, and it (like many databases) could easily be allowed to expand to fill all the disk-space available.