71.17 InvertDecompositionMatrix

InvertDecompositionMatrix(d)

Returns the inverse of the (e--regular part of) d, where d is a decomposition matrix, or crystallized decomposition matrix, of a Hecke algebra or q--Schur algebra. If part of the decomposition matrix d is unknown then InvertDecompositionMatrix will invert as much of d as possible.

gap> H:=Specht(4);; d:=CrystalDecompositionMatrix(H,5);;
gap> InvertDecompositionMatrix(d);
5    

   1                     
4,1  

   .   1                 
3,2  

  -v   .   1             
3,1^2

   .   .   .   1         
2^2,1

 v^2   .  -v   .   1     
2,1^3

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

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