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pieri -- computes a matrix representation for a Pieri inclusion of representations of a general linear group

Synopsis

Description

i1 : pieri({3,1}, {1}, QQ^3) -- removes the first box from the partition {3,1}

o1 = | 3x_0 0    x_1  0    x_2  0    0    0    0       0   0     0    0   
     | 0    3x_0 0    x_1  0    x_2  0    0    0       0   0     0    0   
     | 0    0    2x_0 0    0    0    2x_1 0    x_2     0   0     0    0   
     | 0    0    0    2x_0 0    0    0    2x_1 0       x_2 0     0    0   
     | 0    0    0    0    2x_0 0    0    0    x_1     0   2x_2  0    0   
     | 0    0    0    0    0    2x_0 0    0    0       x_1 0     2x_2 0   
     | 0    0    0    0    0    0    0    x_0  -1/2x_0 0   0     0    3x_1
     | 0    0    0    0    0    0    0    0    0       x_0 -2x_0 0    0   
     ------------------------------------------------------------------------
     0    0    |
     0    0    |
     0    0    |
     0    0    |
     0    0    |
     0    0    |
     x_2  0    |
     2x_1 2x_2 |

                            8                      15
o1 : Matrix (QQ[x , x , x ])  <--- (QQ[x , x , x ])
                 0   1   2              0   1   2
i2 : res coker oo -- resolve this map

                     8                     15                     10                     3
o2 = (QQ[x , x , x ])  <-- (QQ[x , x , x ])   <-- (QQ[x , x , x ])   <-- (QQ[x , x , x ])  <-- 0
          0   1   2             0   1   2              0   1   2              0   1   2         
                                                                                               4
     0                     1                      2                      3

o2 : ChainComplex
i3 : betti oo -- check that the resolution is pure

            0  1  2 3
o3 = total: 8 15 10 3
         0: 8 15  . .
         1: .  . 10 .
         2: .  .  . 3

o3 : BettiTally

See also

Ways to use pieri :