> < ^ Date: Fri, 07 Jul 2000 18:08:19 -0500
< ^ From: Scott Moser <moser@marais.math.lsu.edu >
> ^ Subject: Character Tables and Molien Series

Hi there..

I have a rather simple question that i, unfortunately, could not find
in the manual. I am trying to compute the Molien series of finite
groups under different representations. Dr. Adler's post to the forum
was quite helpfull, but i'm affraid i do not know how to access specific
representaions of a group with it's CharacterTable.

For example:
gap> t:=CharacterTable(PSL(2,5));
CharacterTable( Group([ (3,5)(4,6), (1,2,5)(3,4,6) ]) )
gap> Display(t);
CT1
2  2  2  .  .  .
3  1  .  .  .  1
5  1  .  1  1  .
   1a 2a 5a 5b 3a
2P 1a 1a 5b 5a 3a
3P 1a 2a 5b 5a 1a
5P 1a 2a 1a 1a 3a
X.1     1  1  1  1  1
X.2     3 -1  A *A  .
X.3     3 -1 *A  A  .
X.4     4  . -1 -1  1
X.5     5  1  .  . -1

How would i go about obtaining the Molien series of the _second_
three-dimentional representation, labeled 'X.3'? In general, how do i
reference specific representaions presented in a CharacterTable?

Also, what about reducable representaions? Any idea how to direct sum
the Irreducable representations given in the tabe to form arbitrary
representations?

Thanks much for entertaing my elementary questions,

Scott Moser


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