SInducedModule(x, s)
SInducedModule(x, s, r)
The function SInducedModule, standing for ``string induction'',
provides a more efficient way of r--inducing s times (and a way of
inducing s times if the residue r is omitted); r--induction is
explained in InducedModule.
gap> H:=Specht(4);; SInducedModule(H.P(5,2,1),3); P(8,2,1)+3*P(7,3,1)+2*P(7,2,2)+6*P(6,3,2)+6*P(6,3,1,1)+3*P(6,2,1,1,1) +2*P(5,3,3)+P(5,2,2,1,1) gap> SInducedModule(H.P(5,2,1),3,1); P(6,3,1,1) gap> InducedModule(H.P(5,2,1),1,1,1); 6*P(6,3,1,1)
Note that the multiplicity of each summand of
InducedModule(x,r,...,r) is divisible by <s>! and that
SInducedModule divides by this constant.
As with InducedModule this function can also be applied to elements
of the Fock space (see Specht), in which case the quantum analogue
of induction is used.
See also InducedModule InducedModule. This function requires the
package ``specht'' (see RequirePackage).
GAP 3.4.4