75.1 CartanMat

CartanMat( type, n )

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

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

For type I_2(m), which is in fact an infinity of types depending on the number m, a third argument is needed specifying the integer m so the syntax is in fact CartanMat( "I", 2, m ):

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

CartanMat( type1, n1, ... , typek, nk )

returns the direct sum of CartanMat( type1, n1 ), ldots, CartanMat( typek, nk ). One can use as argument a computed list of types by ApplyFunc( CartanMat, [ type1, n1, ... , typek, nk ] ).

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

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