71.62 InnerProduct

InnerProduct(x, y)

Here x and y are some modules of the Hecke algebra (ie. Specht modules, PIMS, or simple modules). InnerProduct(x, y) computes the standard inner product of these elements. This is sometimes a convenient way to compute decomposition numbers (for example).

gap> InnerProduct(H.S(2,2,2,1), H.P(4,3));
1
gap> DecompositionNumber(H,[2,2,2,1],[4,3]);
1 

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

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