> < ^ Date: Fri, 05 Jan 2001 17:44:12 +0100 (CET)
> < ^ From: Frank Luebeck <frank.luebeck@math.rwth-aachen.de >
< ^ Subject: Re: Symmetric powers of representations

Dear GAP-Forum,

On Wed, 27 Dec 2000, Martin Roetteler wrote:

we would like to compute the multiplicities of the trivial character in the
k-fold symmetric power of a representation of a finite group G over
the finite field GF(2). Could anyone guide us for the appropriate routines
in GAP for doing this.

Martin Roetteler & Chris Charnes

If you know for your group its Brauer character table in characteristic 2,
and if you have the Brauer character of your representation as well, you can
proceed as in the following example:

ct:=CharacterTable("A5") mod 2;
s30 := SymmetricParts(ct, Irr(ct){[4]},30);
Decomposition(Irr(ct), s30, "nonnegative");

If you want to know more details, like `how many trivial constituents are in
the socle?' the question becomes much more difficult. In that case you
probably must use the representation itself and to use the MeatAxe, as
suggested in Derek Holt's answer.

Best regards,

Frank Luebeck

///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\

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