## Models of Representations of Weyl groups

A model of a representation of a group W, with simple reflections
s_{1},...,s_{n}
is a set of matrices
A_{1},...,A_{n} so that
s_{i}-> A_{i} generates the representation.
It is well known that
every representation of a Weyl group has an integral model, i.e. each
matrix A_{i} has integral entries. This generalizes the
result for the symmetric group.

This directory contains models of all irreducible representations of
Weyl groups of low rank, and
software for creating and manipulating these models.

There are two types of models:

Integral Models
The matrices are integral, and the invariant form is not necessarily
diagonal.
These were made by Jeffrey Adams, using Magma.

Rational Seminormal
The matrices are rational, and the invariant form is diagonal.
These are by John Stembridge, using Maple.
Much more information about these models may be found at
Stembridge's site Hereditary Matrix Models
for Weyl Groups

The perl program convert.pl converts between
different kinds of models. Download it and run it yourself; give the
command without any arguments for a help file.

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