The following is a brief report on some difficulties encountered in the
use of the CharTable function to get character tables of Weyl groups
of type D. A problem seems to occur for even rank. An additional
curiosity is that a character table is produced for W(D3) indicating
a group of order 24 whose identity has a centralizer of order 48.

Tom McDonough

=========================================================================

Extracts from various GAP sessions, illustrating some problems
in attempting to generate the character tables for Weyl groups
of type D.

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gap> CharTable("WeylD",4);
Error, Range: <low> must be an integer at
for <var>  in [ i - k + 1 .. i - 1 ] ... in
CharValueSymmetric( n, BetaSet( alpha ), pi ) called from
CharTableSymmetric.irreducibles[1][1]( n / 2, alpha[1], pi[1] / 2
 ) called from
gtab.irreducibles[genchar[i]][genclass[j]]( q, charparam[i], classparam[j]
 ) called from
fun( i ) called from
List( [ 1 .. Length( classparam ) ], function ( j ) ... end ) called from
..
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gap> CharTable("WeylD",6);
Error, Range: <low> must be an integer at
for <var>  in [ i - k + 1 .. i - 1 ] ... in
CharValueSymmetric( n, BetaSet( alpha ), pi ) called from
CharTableSymmetric.irreducibles[1][1]( n / 2, alpha[1], pi[1] / 2
 ) called from
gtab.irreducibles[genchar[i]][genclass[j]]( q, charparam[i], classparam[j]
 ) called from
fun( i ) called from
List( [ 1 .. Length( classparam ) ], function ( j ) ... end ) called from
..
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gap> CharTable("WeylD",8);
Error, Range: <low> must be an integer at
for <var>  in [ i - k + 1 .. i - 1 ] ... in
CharValueSymmetric( n, BetaSet( alpha ), pi ) called from
CharTableSymmetric.irreducibles[1][1]( n / 2, alpha[1], pi[1] / 2
 ) called from
gtab.irreducibles[genchar[i]][genclass[j]]( q, charparam[i], classparam[j]
 ) called from
fun( i ) called from
List( [ 1 .. Length( classparam ) ], function ( j ) ... end ) called from
..
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These commands were successful, but I haven't checked whether the
results are correct.
gap> CharTable("WeylD",5);
gap> CharTable("WeylD",7);
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Finally, an interesting record.
gap> CharTable("WeylD",3);
rec( name := "W(D3)", order := 24, centralizers := [ 48, 8, 8, 4, 6
 ], 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 ] ] ],
  [ 1, [ [ 2, 1 ], [  ] ] ], [ 1, [ [  ], [ 2, 1 ] ] ],
  [ 1, [ [ 3 ], [  ] ] ] ], irredinfo := [ rec(
      charparam := [ 1, [ [ 1 ], [ 1, 1 ] ] ] ), rec(
      charparam := [ 1, [ [  ], [ 1, 1, 1 ] ] ] ), rec(
      charparam := [ 1, [ [ 1 ], [ 2 ] ] ] ), rec(
      charparam := [ 1, [ [  ], [ 2, 1 ] ] ] ), rec(
      charparam := [ 1, [ [  ], [ 3 ] ] ] )
 ], text := "computed using generic character table for Weyl groups of type D"\
, classes := [ 1, 6, 6, 12, 8 ], operations := CharTableOps )
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