> < ^ Date: Fri, 05 Jan 2001 17:32:20 +0100 (CET)
> < ^ From: Frank Luebeck <frank.luebeck@math.rwth-aachen.de >
< ^ Subject: Re: ConstituentsOfCharacter - multiplicities?

Dear GAP-Forum, dear Dima,

On Sat, 30 Dec 2000, Dima Pasechnik wrote:

while ConstituentsOfCharacter gives one a list of irreducible
constituents of a character x, I cannot find a function that
computes the multiplicities of irreducibles in x.

There is a function `MatScalarProducts' which gives you such multiplicities
in case of ordinary (complex) characters.

For a Brauer character table this is more difficult; you can use
`Decomposition' for the task.

An obvious modification of ConstituentsOfCharacter (returning consts
instead of Set(consts)) however does the thing (returning irreducibles with
right multiplicities).

(This remark is only for those who looked at the code in lib/ctblfuns.gi:)
That's not quite right, in `const' each tested character with non-zero
multiplicity is stored. If you test with the list of all irreducibles the
call of `Set(consts)' only sorts the list.

Best regards,


///  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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