weylModulesMap -- build a map between Weyl modules from its action on tableaux

• Usage:

  weylModulesMap(N, M, F)

• Inputs:
  • N, a module, a Weyl module from weylModule
  • M, a module, a Weyl module from weylModule
  • F, a function, a function such that for every Weyl-semistandard filling T in the basis of M, F(T) produces a list of pairs (c, T') with c in ring N and T' a (not-necessarily-standard) filling of the shape of N
• Outputs:
  • a matrix, the $R$-linear map M -> N whose value on each basis tableau is straightened into N

i1 : n = 3;

i2 : R = QQ[x_1..x_n];

i3 : M = weylModule({2}, R^n);

i4 : N = weylModule({2,1}, R^n);

i5 : F = T -> apply(numgens R, k -> (R_k, augmentWeylFilling(T, 1, k)));

i6 : weylModulesMap(N, M, F)

o6 = | x_2 -x_1 0    0    0    0    |
     | x_3 0    0    -x_1 0    0    |
     | 0   x_2  -x_1 0    0    0    |
     | 0   x_3  0    0    -x_1 0    |
     | 0   0    x_3  0    -x_2 0    |
     | 0   0    0    x_2  -x_1 0    |
     | 0   0    0    x_3  0    -x_1 |
     | 0   0    0    0    x_3  -x_2 |

             8      6
o6 : Matrix R  <-- R