Given a list L of partitions {L1,...,Ln} computes the character of the composition of Schur functors SL1(SL2(...(SLn(V)))) applied to the canonical representation of GL(V) where dim(V)=d
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 3 3 2 3 2 3 3 3 4 4 o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x + x x + 2x x x + 2x x x + x x + x x x + x 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 0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 3 4 4 3 2 2 3 4 3 2 2 2 2 2 + 2x x x + 2x x x + x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x + 5x x x x + 5x x x x + 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 3 3 2 3 4 4 3 2 2 2 2 3 2 3 2 2 2 2 2 2x x x + 2x x x + 4x x x x + 2x x x + x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x + 5x x x x + 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 3 2 2 2 2 2 2 2 2 2 3 2 3 2 3 3 2 3 2 3 3 3 2 3 3 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x + x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3 0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 ---------------------------------------------------------------------------------------------------------------------------- 2 3 2 3 2 3 3 3 4 4 4 2x x x + 2x x x + 2x x x + x x + x x x + x x x + x x x 1 2 3 0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3 o1 : QQ[x ..x ] 0 3 |
The object character is a method function.