Character Tables of Weyl Groups in GAP
======================================

An extensive description of  the implementation of character tables of
Weyl groups  in   GAP  is now   available  via  anonymous   'ftp' from
'samson.math.rwth-aachen.de'.

The  text  cites  the  main  results  from  representation  theory  of
symmetric groups following

  G. James, A. Kerber: The representation theory of the symmetric
  group, Addison-Wesley 1981.

Some results which are not easily found in the literature  are proved,
like  a  theorem  about  character  values  of  wreath  products  with
symmetric  groups and a theorem about  character values of Weyl groups
of type  D.  Moreover  the text  contains  all  GAP programs  that are
needed for the implementation.  Some time critical functions are given
in  several  versions.   This shows  how  mathematical formulas can be
translated  in a  straight forward  way  into GAP  code and how a  GAP
function can be improved.  Moreover the concept of a generic character
table in GAP is used and explained in some detail.

The original text is in  the file 'ctweyl.xpl' which is written in GAP
readable form.  Thus the programs mentioned in the text need not to be
typed in but can  be read  by GAP directly from  the file.   From this
text a TeX  file 'ctweyl.tex' can be  produced  with a the AWK  script
'xpl2tex' by the command sequence

   xpl2tex ctweyl.xpl > ctweyl.tex

Together with the TeX style file  'gap-xpl.sty' the resulting file can
be  processed with 'latex'.  This gives  a file  'ctweyl.dvi' which is
also available via 'ftp'.

This description consists of the following files.

   'ctweyl.xpl':    the source code of both the text and the programs
                    in GAP readable format.

   'ctweyl.dvi':    the 'dvi' file of the text.

   'xpl2tex':       an AWK script which produces a TeX file from
                    'xpl' input.

   'gap-xpl.sty':   a TeX style file for GAP example files.



How to write a 'xpl' file.
==========================

Other GAP users are  encouraged  to  produce  similar descriptions  of
their GAP functions.   Here  the following rules for '.xpl' files have
to be regarded.

* The first line accepted by 'xpl2tex' is an emty line.

This means that you can put an arbitray amount of comment lines at the
beginning of your '.xpl' file.

* The next line should look like

   '##  \documentstyle[11pt,gap-xpl]{article}'

This  will be  the first line of the  TeX file.  It includes the style
file 'gap-xpl.sty' and chooses 11pt as the text size.

* Each line containing TeX code should start with the sequence '##  '.

This will be a comment  for GAP while 'xpl2tex' will recognize this as
text and will delete the first four letters of that line.

* GAP code is entered in  the same way as in GAP library files.

* A sequence of GAP code must be preceded (and terminated) by an empty 
line.

'xpl2tex' will put each sequence of lines not starting with '##' in an
indented verbatim environment.

* The style file 'gap-xpl.sty' allows abbreviations for special fonts.

'text' will produce text in typewriter font.

*text* will produce text in bold face.

<text> will produce text in italic font.

|text| will produce text in a 10pt verbatim environment