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schurModulesMap -- creates a map between two Schur modules via the specified function.

Synopsis

Description

Constructs the map between M and N specified by the function F.

i1 : n = 4;      --j-th differential of the Koszul Complex on the variables of R
i2 : j = 2;
i3 : mu1=apply(j,j->1)

o3 = {1, 1}

o3 : List
i4 : mu2=apply(j+1,j->1)

o4 = {1, 1, 1}

o4 : List
i5 : R = QQ[x_1..x_n];
i6 : M=schurModule(mu1,R^n);
i7 : N=schurModule(mu2,R^n);
i8 : F = T -> apply(numgens R, j -> (R_j, augmentFilling(T,0,j)))

o8 = F

o8 : FunctionClosure
i9 : schurModulesMap(N,M,F)

o9 = | x_3 -x_2 x_1 0    0    0   |
     | x_4 0    0   -x_2 x_1  0   |
     | 0   x_4  0   -x_3 0    x_1 |
     | 0   0    x_4 0    -x_3 x_2 |

             4      6
o9 : Matrix R  <-- R

Caveat

The function F should output lists of pairs where the second component is a filling of the partition corresponding to N.

See also

Ways to use schurModulesMap :

For the programmer

The object schurModulesMap is a method function.