> < ^ Date: Tue, 16 Nov 1993 11:38:23 +0100
> < ^ From: Goetz Pfeiffer <Goetz.Pfeiffer@NUIGalway.ie >
^ Subject: Character Tables of Weyl Groups.

Together with the new release 3.3 of GAP a description of the
character tables of Weyl groups in GAP is now available via 'ftp'.
The 'dvi' file is found in 'pub/gap/split/dvi3r3p0.zoo', the other
relevant files mentioned below are part of
'pub/gap/split/etc3r3p0.zoo'. This message includes 'ctweyl.doc'.
Any comments and suggestions are very welcome.

Geotz Pfeiffer.


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

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

'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

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