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SchurFunctors :: character

character -- Determines the character of a compostion of schur functors applied to the representation of GL(V) on V

Synopsis

Description

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
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

See also

Ways to use character :

For the programmer

The object character is a method function.