75.2 CartanType

CartanType( C )

CartanType( D )

returns the type of the Cartan Matrix C. The result is a list each element of which describes an irreducible component of C, as pair [type,indices] where type is the type ("A", "B", "D", etcldots) of the component and indices the indices in C where it sits, so that

C{indices}{indices} = CartanMat( type, Length( indices ) )

A triple [type, indices, m] is actually returned for a component of type I_2(m). The indices are arranged in the standard order in which we give Dynkin diagrams.

    gap> C := [ [ 2, 0, -1 ], [ 0, 2, 0 ], [ -1, 0, 2 ] ];;
    gap> CartanType( C );
    [ [ "A", [ 1, 3 ] ], [ "A", [ 2 ] ] ] 

The argument to CartanType can also be a domain (i.e., D should be a record with a field operations.CartanType, and that function is then called with D as argument --- this is used for Coxeter groups and Coxeter cosets).

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

Previous Up Top Next
Index