71.22 DecompositionMatrixMatrix

DecompositionMatrixMatrix(H, m, n)

Given a Hecke algebra H, a GAP matrix m, and an integer n this function returns the Specht decomposition matrix corresponding to m. If p is the number of partitions of n and r the number of e--regular partitions of n, then m must be either <r>times<r>, <p>times<r>, or <p>times<p>. The rows and columns of m are assumed to be indexed by partitions ordered by H.Ordering (see Specht).

gap> H:=Specht(3);;
gap> m:=[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 1, 0 ], 
>         [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ] ];;
gap> DecompositionMatrixMatrix(H,m,4);
4    

 1       
3,1  

 . 1     
2^2  

 1 . 1   
2,1^2

 . . . 1
1^4  

See also DecompositionMatrix DecompositionMatrix and MatrixDecompositionMatrix MatrixDecompositionMatrix. This function requires the package ``specht'' (see RequirePackage).

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