[GAP Forum] Brauer Table for L2(128)

Frank Luebeck frank.luebeck at math.rwth-aachen.de
Fri Apr 30 17:08:01 BST 2004

On Thu, 29 Apr 2004, Chris Bates wrote:

> Does anybody know if the mod 2 Brauer character table for L_{2}(128) is
> available anywhere?

Dear Chris, dear Forum,

I don't know of such an explicit table. But it is not too difficult to
construct it. Even all irreducible representations are not difficult
to construct:

One needs the natural representation of G = SL_{2}(128) as 2x2 matrices over
GF(128). Steinbergs tensor product theorem says how all irreducible
representations are constructed; they are tensor products of the
Frobenius twists of this fixed natural representation. This description
can also be used to write down the corresponding Brauer characters.

If you think the explicit Brauer table is useful for this case
(the values give a 128x128 matrix with unpleasant root of unity terms)
and need help with a short GAP program along the lines above, don't
hesitate to contact me.

Best regards,


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

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