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

Synopsis

• Usage:

  schurModulesMap(N,M,F)

• Inputs:
  • N, a module, Schur module
  • M, a module, Schur module
  • F, a function, The function should specify, for every SST in the basis of M, a linear combination of tableaux of the shape specified by N. The output of F should be a sequence of pairs (c,T) where c is a coefficient in ring(N) and T a tableau (not necessarily semistandard).
• Outputs:
  • G, a matrix, A map between M and N.

Description

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

See also

• schur -- creates a map between Schur modules