71.11 SInducedModule

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).

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GAP 3.4.4
April 1997