81.2 HeckeSubAlgebra

HeckeSubAlgebra( H, r )

Given an Hecke Algebra H and a set of roots of Group(H) given as their index in the roots, return the Hecke sub-algebra generated by the T_s corresponding to these roots. The roots must be simple roots if any parameter is not 1.

As for Subgroup, a subalgebra of a subalgebra is given as a subalgebra of the parent algebra.

    gap> u := X( Rationals );; u.name := "u";;
    gap> H := Hecke( CoxeterGroup( "B", 2 ), u );
    Hecke(CoxeterGroup("B", 2),[ u, u ],[  ])
    gap> HeckeSubAlgebra( H, [ 1, 4 ] );
    Hecke(ReflectionSubgroup(CoxeterGroup("B", 2), [ 1, 2 ]),[ u, u ],
    [  ])
    gap> HeckeSubAlgebra( H, [ 1, 7 ] );
    Error, Generators of a sub-Hecke algebra should be simple reflections 
    in HeckeSubAlgebra( H, [ 1, 7 ] ) called from main loop
    brk> 

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

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