GAP Manual: 63.1. CartanMat

CartanMat( type, n )

returns the Cartan matrix of Dynkin type type and rank n. Admissable types are the strings "A", "B", "C", "D", "E", "F", "G", "H", "I2". 

    gap> CartanMat( "F", 4 );;
    gap> PrintArray( last );
    [ [   2,  -1,   0,   0 ],
      [  -1,   2,  -1,   0 ],
      [   0,  -2,   2,  -1 ],
      [   0,   0,  -1,   2 ] ]

    gap> CartanMat( "I2", 5 );
    [ [ 2, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, 2 ] ]

(this gives the dihedral group of order 10, so the integer 5 is not the rank in this case.)

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

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