i1 : character({{1,1,1},{2}},4)--The GL(4) action on the Grassmannian of 3-dimensional subspaces of quadrics in four variables
3 3 4 3 2 2 3 4 3 2 2 2 2 3 2
o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x
0 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 4 4 3 2 2 3
+ x x + 2x x x + 2x x x + x x + x x x + x x x + 2x x x + 2x x x
0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 0 1 3 0 1 3
------------------------------------------------------------------------
4 4 3 2 2 3 4 3 2
+ x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x
0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3
------------------------------------------------------------------------
2 2 2 2 3 2 2 3 3 2 3
+ 5x x x x + 5x x x x + 2x x x + 2x x x + 4x x x x + 2x x x +
0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
4 4 3 2 2 2 2 3 2 3 2 2 2
x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x +
0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3
------------------------------------------------------------------------
2 2 3 2 2 2 2 2 2 2 2 2 3 2 3 2
5x x x x + 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x
0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 2 3 3 2 3
+ x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 2x x x +
0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
2 3 2 3 3 3 4 4 4
2x x x + 2x x x + x x + x x x + x x x + x x x
0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3
o1 : QQ[x ..x ]
0 3
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