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SPECHT 2.4                                October 1997
    A package for calculating decomposition numbers of
    Hecke algebras of the symmetric groups and q-Schur
    algebras.

(C) Andrew Mathas  mathas@maths.usyd.edu.au     Sydney
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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 
in \Specht s <doc> directory.

Specht is a GAP share library package; it is made available
only under the usual terms and conditions of GAP.
 
Andrew Mathas
Sydney, Ocotber 1997


Description:
------------

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 [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 
include\:

  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.

\psection{Installing \Specht}

When you unpack \Specht\ you will find the following files in a 
directory called specht-2.2\:

|README      -this file
doc/         -LaTeX source for the manual (see below)|
gap/         -|\GAP| source
init.g       -initization file
lib/         -Specht library files

Ideally, \Specht\ should be installed in the \GAP\ packages directory (in 
a subdirectory called ``specht\'\'); however, it can be installed anywhere. 
If \Specht\ is not installed in \GAP\ packages directory then include a
line of the form

| Add(PKGNAME, "/path/to/directory/containing/specht/"); 
  PKGNAME:=Reversed(PKGNAME); |

in your .gaprc in your home directory (create such a file with this line if
you don't already have one). \Specht\ is now ready to use.

\Specht\ is now installed and ready to use\:

|gap> RequirePackage("specht");
gap> H:=Specht(3);
Specht(e=3, S(), P(), D(), Pq())|

\bigskip

*Installing \Specht\'s online documentation*

\bigskip

The documentation for Specht can be found in the subdirectory 'doc'. The
more inportant files in this directory are\:

|specht.tex  -LaTeX source for the manual
specht.html -a HTML version of the manual
manual.tex  -header file for LaTeXing specht.tex 
install.tex -these installation notes|

To install the *online* documentation for Specht proceed as 
follows\:

|1. Copy |<specht.tex>| into the |\GAP\ <doc/>| directory, 
2. Change directory to |\GAP|s <doc/> directory and add the line
   |<$\backslash$Include\{specht\}>| to |<manual.tex>|.
3. |\LaTeX\ <manual.tex>|.
4. Run |'makeindex'| (if available) and repeat 3. |

A copy of just the \Specht\ manual can be obtained by \LaTeX ing the
file <manual.tex> in \Specht s <doc/> directory.

\bigskip

Finally, if you have any questions or problems please email me.
The latest version of \Specht\ can be obtained from
|http://www.ma.ic.ac.uk/~apmath/specht|.

\bigskip

Andrew Mathas\\ 
a.mathas@ic.ac.uk
