71.27 SimpleDimension

SimpleDimension(d)
SimpleDimension(H, n)
SimpleDimension(H|d, mu)

In the first two forms, SimpleDimension prints the dimensions of all of the simple modules specified by d or for the Hecke algebra 'H'(Sym_n) respectively. If a partition mu is supplied, as in the last form, then the dimension of the simple module D(mu) is returned. At present the function is not implemented for the simple modules of the q--Schur algebras.

gap> H:=Specht(6);;
gap> SimpleDimension(H,11,3);
272
gap> d:=DecompositionMatrix(H,5);; SimpleDimension(d,3,2);
5
gap> SimpleDimension(d);
5     : 1
4,1   : 4
3,2   : 5
3,1^2 : 6
2^2,1 : 5
2,1^3 : 4
1^5   : 1

This function requires the package ``specht'' (see RequirePackage).

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