76.10 HighestShortRoot

HighestShortRoot( W )

Let W be an irreducible Coxeter group. HighestShortRoot computes the unique short root of maximal height of W. Note that if all roots have the same length then this is the unique root of maximal height, which can also be obtained by W.roots[W.N]. An error message is returned for W not irreducible.

    gap> W := CoxeterGroup( "G", 2 );;  W.roots;
    [ [ 1, 0 ], [ 0, 1 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], 
      [ -1, 0 ], [ 0, -1 ], [ -1, -1 ], [ -1, -2 ], [ -1, -3 ], 
      [ -2, -3 ] ]
    gap> HighestShortRoot( W );
    4
    gap> W1 := CoxeterGroup( "A", 1, "B", 3 );;
    gap> HighestShortRoot( W1 );
    Error,  group is not irreducible
     in
    HighestShortRoot( W1 ) called from
    main loop
    brk> 

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

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