RestrictedModule(x)
RestrictedModule(x, r_1 [, r_2, ...])
Given a module x for 'H'(Sym_n) RestrictedModule returns the
corresponding module for 'H'(Sym_{n-1}). The restriction of the
Specht module S(mu) is the linear combination of Specht modules
sum 'S'(<nu>) where nu runs over the partitions whose
diagrams are obtained by deleting a node from the diagram of
mu. If only nodes of residue r are deleted then this
corresponds to first restricting S(mu) and then taking one of
the block components of the restriction; this process is known as
r-restriction (cf. r--induction in InducedModule).
There is also a function SRestrictedModule (see SRestrictedModule)
which provides a faster way of r--restricting s times (and
restricting s times).
When more than one residue if given to RestrictedModule it returns
RestrictedModule(x,r_1,r_2,...,r_k)=
RestrictedModule(RestrictedModule(x,r_1),r_2,...,r_k)
(cf. InducedModule InducedModule).
gap> H:=Specht(6);; RestrictedModule(H.P(5,3,2,1),4); 2*P(4,3,2,1) gap> RestrictedModule(H.D(5,3,2),1); D(5,2,2)
``Quantized'' restriction
As with InducedModule, when RestrictedModule is applied to the
canonical basis elements H.Pq(mu) a quantum analogue of
restriction is applied; this time, RestrictedModule(*,i)
corresponds to the action of the generator E_i of
U_q(widehat{sl_e}) on F [LLT].
See also InducedModule InducedModule, SInducedModule
SInducedModule, and SRestrictedModule SRestrictedModule. This
function requires the package ``specht'' (see RequirePackage).
GAP 3.4.4