## Integral Models of Representations of Weyl groups

Here are integral models of the following Weyl groups.

Each directory contains some or all of the following files:

dynkinDiagram: gives numbering of the generators of W
characterTable: gives the numbering of representations
conjugacyClasses: as integral matrices of size rank(W), in the reflection representation of W
Zn: integral model of representation #n, standard magma format
ZnCpt: integral model of representation #n, compact magma format
Zn/QnCpt: rational model of representation #n, standard magma format, if Zn isn't available
Report: information on the models
initData: file to be read into magma to initialize computations.
tests: directory containing output of tests of each model
The smaller of the two files Zn/ZnCpt are included.
Each file Zn contains a list of matrices, each given by a list of n^{2} numbers, one for each
generator, and the matrix F of the invariant form.
For example here is the two--dimensional representation Z3 of W(A_{2}), as a list of 2 2x2 matrices, and F:

operators:=[
[-1,0,1,1],[1,1,0,-1]];

F:=[2,-1,-1,2];

The information in ZnCpt is similar. The non-zero entries in each matrix are given by run lengths: [a1,a2,a3,a4,... means the matrix with a2 in position
a1, followed by a4 in position a1+a2...

The previous example in compact format is:

operators:=[
[1,-1,2,1,1,1],
[1,1,1,1,2,-1]];

F:=[2,-1,-1,2]

Software used in making the models. This uses the
commercial software package Magma

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