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In his message of 13 May 1993 Tom McDonough desrcibes

some difficulties encountered in the

use of the CharTable function to get character tables of Weyl groups

of type D.

These problems came into the package with the new concept for strings

in GAP.

The classes and characters of Weyl groups of type D are labelled by

pairs of partitions. For even rank certain labels occur twice. They

are distinguished by a "+" or "-" sign in the place of the second

partition. The functions for the constuction of the character table

try to recognise these signed labels by 'IsString(pi[2])'.

But the second partition may also be empty, represented by the empty

list. And due to the new string concept, the empty list is now

recognised as a string, too. This leads to the problems encountered

by Tom McDonough.

This will be fixed with the next upgrade. Then the signs in the

labels will no longer be strings but single characters: '+' and '-'.

This means 'CharTable("WeylD", <n>)' and 'CharTable("Alternating",

<n>)' will then produce slightly different results. I hope this

causes no problems.

In the meantime a possible workaround is to replace the function

'IsString' by one that ignores the empty list:

gap> IsStr:= IsString;

function (...) internal; end

gap> IsString:= function(obj)

> return obj <> [] and IsStr(obj); end;

function ( obj ) ... end

WARNING: This might have side-effects in places where the empty string

is relevant.

But now it is possible to compute the tables and centralizers are

no longer bigger than the whole group.

gap> CharTable("WeylD", 3); rec( name := "W(D3)", order := 24, centralizers := [ 24, 8, 4, 4, 3 ], orders := [ 1, 2, 2, 4, 3 ], powermap := [ , [ 1, 1, 1, 2, 5 ], [ 1, 2, 3, 4, 1 ] ], irreducibles := [ [ 3, -1, -1, 1, 0 ], [ 1, 1, -1, -1, 1 ], [ 3, -1, 1, -1, 0 ], [ 2, 2, 0, 0, -1 ], [ 1, 1, 1, 1, 1 ] ], classparam := [ [ 1, [ [ 1, 1, 1 ], [ ] ] ], [ 1, [ [ 1 ], [ 1, 1 ] ] ], ...

Goetz Pfeiffer.

PS: a detailed description of the implementation of the character

tables of Weyl groups and related groups will soon be available via

anonymous ftp from 'samson.math.rwth-aachen.de'.

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