HWModule is broken

[andrey-krutov]

The HWModule function is broken: the commutation table for the negative root vectors is incomplete.

Example:

CM = ({
   {2, -1, -1},
   {-1, 2, 0},
   {-1, 0, 2}
  })
CartanMatrixAlgebra[g, {x, h, y}, CM]
HWModule[v, g, {1, 0, 0}]
Table[Act[xx, vv], {xx, Basis[g]}, {vv, Basis[v]}]

Output for the commutation table:

{{v , - v , 0, 0, v , - v }, {0, v , - v , v , - v , 0}, {0, v , v , - v , - v , 0}, 
   1     2         5     6        2     3   4     5           2   3     4     5
   {0, v , 0, 0, 0, v }, {0, 0, - v , 0, v , 0}, {0, 0, 0, - v , v , 0}, 
        1            5             2      4                   2   3
   {0, 0, - v , 0, 0, - v }, {0, 0, 0, - v , 0, - v }, {0, 0, 0, 0, v , v }, 
             1           4                1        3                 1   2
   {v , 0, 0, 0, v , 0}, {0, - v , 0, v , 0, 0}, {0, - v , v , 0, 0, 0}, 
     2            6             3      5                4   5
   {v , 0, 0, v , 0, 0}, {v , 0, v , 0, 0, 0}, {v , v , 0, 0, 0, [y ,v ]}}
     3         6           4      6              5   6             6  6