This is a page on GAP 3, which is
still available, but no longer supported. The present version is
GAP 4 (See
Status of GAP 3). 
GAP 3 Share Package "specht"
Specht: Decomposition matrices for the Hecke algebras of type A
Share package since release 3.4, about July 1996,
communicated by Herbert Pahlings.
This package has been transferred to GAP 4 by Dmitriy Traytel.
The GAP 4 version is called Hecke.
Author
Andrew Mathas.
Implementation
Language: GAP 3
(Note: Specht is not compatible with GAP 4.)
Operating system: Any
Current version: 2.4
Description
A package for calculating decomposition numbers of Hecke algebras
of the symmetric groups and qSchur algebras.
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 this package.
These programs grew out of the attempts by Gordon James and myself
to understand the decomposition matrices of Hecke algebras of type A
when q = 1. The package is now much more general and its' highlights
include:

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.

For Hecke algebras defined over fields of characteristic zero we
have implemented the algorithm of Lascoux, Leclerc, and Thibon 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.

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.

The qanalogue of Schaper's theorem is included, as is
Kleshchev's [K] algorithm of calculating the Mullineux map. Both are
used extensively when inducing decomposition matrices.

Specht can be used to compute the decomposition numbers of
qSchur algebras (and the general linear groups), although there is
less direct support for these algebras. The decomposition matrices for the
qSchur algebras defined over fields of characteristic zero for n < 11
and all e are included in Specht.

The LittlewoodRichard 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.

The decomposition matrices for the symmetric groups Sym_n are
included for n < 15 and for all primes.
Home Page
Specht
Manual
You can reach the HTML version of the
Specht 2.4 manual given on the Specht Home Page. Note that
chapter 71 of the
GAP 3 manual
describes an earlier version.
Contact address
Andrew Mathas University of Sydney
Sydney
Australia
email: mathas@maths.usyd.edu.au
