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^ Subject:

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

www at

http://www.ma.ic.ac.uk/~apmath/abstracts/specht.html

Below I include the README file for your perusal.

Best regards,

Andrew Mathas

----

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 a.mathas@ic.ac.uk 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

in specht.ps.

Specht is a GAP share library package; it is made available

only under the usual terms and conditions of GAP.

Andrew Mathas

London March 1996

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.

Installation: -------------

When you unpack Specht you should find the following files

README -this file

init.g -GAP source

specht.g

symmcomb.g

tableaux.g

tex.g

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:

SPECHTHOME:="/usr/local/lib/gap/pkg/specht/";

(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

specht.tex

into the GAP doc/ directory, adding the line

\Include{specht}

to the end of <manual.tex>, and then re-LaTeXing the manual.

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