> < ^ Date: Wed, 06 Dec 1995 16:56:05 +0000
> < ^ From: Andrew Mathas <mathas@maths.su.oz.au >
^ Subject: package for calculating decomposition numbers of Hecke algebras

Dear GAP forum,
this is a 'short' note to announce a new GAP package for calculating
decomposition numbers of the Iwahori-Hecke algebras of symmetric groups.
I have just uploaded the package to samson.math.rwth-aachen.de where
it appears in the /pub/incoming directory under
This file is a shar file; to extract the package proceed as follows:
1. gunzip specht.uu.gz
2. sh specht.uu
This will install SPECHT in your current directory (there are a large
number of library files, containing decomposition matrices, coming to
slightly over 1Mb). (non-UNIX users will have to gunzip the file, uudecode
it and use tar by hand, and then edit specht.g to set SPECHTHOME
The package can be used for
1. Calculating decomposition matrices of Hecke algebras of
the symmetric groups (mainly useful in characteristic 0;
but applicable more generally).
2. Calculating decomposition matrices of symmetric groups. The
decomposition matrices of S_n for the primes 2, 3, and 5
and n < 16 are included (and for "small" (n,p) are readily
calculated using the package).
3. Calculating decomposition matrices of q-Schur algebras,
although this is not fully supported as yet (no routines for
dealing with singular partitions yet exist)
Effectively, the package allows computations to be made in the Grothendiek
ring of these algebras. In addition, many of the combinatorial tools from
the representation theory of symmetric groups are implements in the
package; for example, routines for calculating quotients
and cores of partitions, the (inverse) Littlewood-Richard rule, listing
(semi-)standard tableaux (not documented at present; the commands are
SemistandardStableaux(nu,mu) and StandardTableaux(mu) ), inducing and
restricting specht modules, PIMs, and simple modules, "inducing"
decomposition matrices, the q-Schaper theorem, Mullineux's map, dimension
formulae for these modules,... are to be found in the package.

Documentation for the package is to be found in the file specht.ps; this can
be made available through GAP's online help by letting the GAP manual.tex
know about the included file specht.tex (you will need to add a
\Include{specht} to manual.tex and re-LaTeX the manual).

At this stage the package should be considered a beta release. Currently
I am rewriting part of the package so that it makes use of a recent
conjecture (now proved by Grojnowski) for calculating decomposition matrices
of Hecke algebras over fields of characteristic 0; the basic algorithm is
written, but I have yet to fully integrate this into the package; I hope to
do this by the end of January 1996.

I would very much like to hear any comments and criticisms on the package,
and suggestions for improvements or extensions. Ultimately I would like to
add full support for calculations for Hecke algebras over finite fields,
q-Schur algebras, and general linear groups (this will not happen for quite
some time however...). Any comments on the interface or regarding any
obviously 'missing' functions are particularly welcome.

As mentioned above, I hope to have the package finished, complete with the
LLT conjecture early next year. Until then, I would much appreciate
comments and criticisms.

Andrew Mathas
Imperial College

We are all of us in the gutter, but some of us are looking
at the stars.
                                               Oscar Wilde

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