Braid( W )( s1, .., sn )
Braid( W )( list [, pw0 ])
Braid( W )( p [, pw0 ])
Let W be a Coxeter group and let w be an element of W, represented
as a permutation p of the roots, or as a sequence s_1,..,s_n of
integers representing a (non necessarily reduced) word in the generators
of W. The calls above return the element of the braid monoid of W
defined by w. If pw0 (a positive or negative integer) is given, the
resulting element is multiplied in the braid group by bw_0^{pw0}. The
result of Braid(W) is a braid-making function, which can be assigned to
make conveniently braid elements as in the example below.
A braid element bb corresponding to the Coxeter group W is
represented as a record with fields pw0, elm and operations. elm
represents an element bx in B^+, and elm and pw0 are such that
bb=bw_0^{text{pw0}}bx and bw_0^{-1}bxnotin B^+. elm is a
sequence of elements of W (permutations of the roots), which are the
image in W of alpha(bb), alpha(alpha(bb)^{-1}bb),ldots.
Operations for braid elements.
gap> CHEVIE.PrintBraid := "Deligne";;
gap> W := CoxeterGroup( "A", 3 );;
gap> B := Braid( W );
function ( arg ) ... end
gap> B( W.generators[1] );
1
gap> B( 2, 1, 2, 1, 1 );
121.1.1
gap> B( [ 2, 1, 2, 1, 1 ], -1 );
w0^-1.121.1.1
This function requires the package "chevie" (see RequirePackage).
GAP 3.4.4