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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.

(goetz@math.rwth-aachen.de)

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