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 n2 numbers, one for each generator, and the matrix F of the invariant form.

    For example here is the two--dimensional representation Z3 of W(A2), as a list of 2 2x2 matrices, and F:

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

    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]];

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

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