Dear Ms and Mr Gap:
I have just uploaded the new version of my package for calculating
decomposition numbers of Hecke algebras, q-Schur algebras, and symmetric
groups to samson.math.rwth-aachen.de; it can be found in the incoming
directory as specht-2.0.tar.gz. The package can also be obtained via the
Below I include the README file for your perusal.
A mathematician is a device for turning coffee into theorems.
------------------------------------------------------ SPECHT 2.0 March 1996 A package for calculating decomposition numbers of Hecke algebras of the symmetric groups and q-Schur algebras. (C) Andrew Mathas firstname.lastname@example.org Imperial College ------------------------------------------------------
For installation notes see below. What follows is a brief
description of the package; more details can be found in
the manual, a postscript version of which can be found
Specht is a GAP share library package; it is made available
only under the usual terms and conditions of GAP.
London March 1996
This package contains functions for computing the decomposition matrices
for Hecke algebras of the symmetric groups. As the (modular)
representation theory of these algebras closely resembles that of the
(modular) representation theory of the symmetric groups --- indeed, the
later is a special case of the former --- many of the combinatorial tools
from the representation theory of the symmetric group are included in
These programs grew out of the attempts by Gordon James and myself [JM1]
to understand the decomposition matrices of Hecke algebras of type *A*
when $<q>=-1$. The package is now much more general and its\'\ highlights
1. \Specht\ provides a means of working in the Grothendieck ring of a
Hecke algebra <H> using the three natural bases corresponding to the
Specht modules, projective indecomposable modules, and simple modules.
2. For Hecke algebras defined over fields of characteristic zero we
have implemented the algorithm of Lascoux, Leclerc, and Thibon [LLT] for
computing decomposition numbers and ``crystallized decomposition
matrices\'\'. In principle, this gives all of the decomposition matrices
of Hecke algebras defined over fields of characteristic zero.
3. We provide a way of inducing and restricting modules. In addition,
it is possible to ``induce\'\'\ decomposition matrices; this function is
quite effective in calculating the decomposition matrices of Hecke
algebras for small <n>.
4. The <q>--analogue of Schaper\'s theorem [JM] is included, as is
Kleshchev\'s [K] algorithm of calculating the Mullineux map. Both are
used extensively when inducing decomposition matrices.
5. \Specht\ can be used to compute the decomposition numbers of
<q>--Schur algebras (and the general linear groups), although there is
less direct support for these algebras. The decomposition matrices for the
<q>--Schur algebras defined over fields of characteristic zero for $n\<11$
and all <e> are included in \Specht.
6. The Littlewood--Richard rule, its inverse, and functions for many
of the standard operations on partitions (such as calculating cores,
quotients, and adding and removing hooks), are included.
7. The decomposition matrices for the symmetric groups $\Sym_n$ are
included for $n\<15$ and for all primes.
When you unpack Specht you should find the following files
README -this file
init.g -GAP source
lib/ -Specht library files
specht.ps -postscript version of Specht manual
specht.tex -LaTeX version of Specht manual
Ideally, Specht should be installed in GAP the packages directory,
however, it can be installed anywhere. Once the files have been
placed in the desired directory edit the file <init.g> and set
the variable 'SPECHTHOME' to the name of the current directory.
Usually, this will be something like:
(which is the default).
Specht is now installed and ready to use\: |gap> RequirePackage("specht"); gap> H:=Specht(3); Specht(e=3, S(), P(), D(), Pq())|
The online documentation can be installed by first copying
into the GAP doc/ directory, adding the line
to the end of <manual.tex>, and then re-LaTeXing the manual.