> < ^ Date: Thu, 16 Dec 1993 14:02:30 +0100
> < ^ From: Goetz Pfeiffer <Goetz.Pfeiffer@NUIGalway.ie >
< ^ Subject: Re: Naive CharTable question

Steve Fisk writes in his message of 14-Dec-93:

I'm interested in the eigenvalues of the representation (not just for
S4, but for larger symmetric groups as well), I was pleased to find
the function "Eigenvalues". My question is this:

I would like a function f(i,j) that does the following:

1) prints the partition of 4 corresponding to the i-th
irreducible representation of S4.
2) prints the partition of 4 corresponding to the j-th
conjugacy class of S4.
3) prints Eigenvalues(t,t.irreducibles[i],j) (this is the easy part)

Is this feasible?

The following code will produce a function which satisfies roughly 1)
to 3). (There are some cosmetical additions in order to make the
output more readable, note the final argument "\n" of 'Print' which
starts a new line after printing the data).

gap> t:= CharTable("Symmetric", 4);;
gap> p:= Partitions(4);;
gap> f:= function(i, j)
> Print(p[i], " ", p[j], ": ", Eigenvalues(t, t.irreducibles[i], j), "\n");
> end;
function ( i, j ) ... end

This function 'f' works for all symmetric groups, only the values of
't' and 'p' have to be prepared. Note that this function 'f' doesn't
return a value. It just prints characters on the screen. So the data
computed by 'Eigenvalues', eg., are lost for further use.

A detailed description of the implementation of Chartacter tables of
Weyl groups in GAP is found in the article 'Character Tables of Weyl
Groups in GAP' which is part of the distribution of GAP-3.3 in form of
the files 'ctweyl.dvi' and ctweyl.xpl'.

Goetz Pfeiffer.

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