76.17 MatYPerm

MatYPerm( W, w )

Let w be a permutation of the roots of the Coxeter datum W acting on the vector space Vdual. MatYPerm returns the matrix of a linear transformation of Vdual which acts trivially on the orthogonal of the roots and has same effect as w on the simple coroots. Only the image of the simple coroots by w is used.

We continue the example from MatXPerm and obtain:

    gap> my := MatYPerm( W, w0 );
    [ [ 0, 0, 0, 0, 0, -1, 0 ], [ 0, -1, 0, 0, 0, 0, 0 ],
      [ 0, 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, -1, 0, 0, 0 ],
      [ 0, 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0, 0 ],
      [ 1, 2, 3, 4, 3, 1, 1 ] ] 

This function requires the package "chevie" (see RequirePackage).

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