next | previous | forward | backward | up | top | index | toc | directory | Macaulay 2 web site

saturatePieri -- computes a matrix representation for a Pieri inclusion modulo p of representations of a general linear group

Synopsis

Description

i1 : saturatePieri({3,1}, {1}, QQ^3, 5) -- removes the first box from the partition {3,1}, then reduces mod 5

o1 = | x_0 0   x_1  0   0    x_2  0   0    0   0   0    0   0   0    0   |
     | 0   x_0 0    0   x_1  0    0   x_2  0   0   0    0   0   0    0   |
     | 0   0   2x_0 x_1 0    0    x_2 0    0   0   2x_2 0   0   0    0   |
     | 0   0   0    0   2x_0 0    x_1 0    x_2 0   -x_1 0   x_2 0    0   |
     | 0   0   0    0   0    2x_0 x_1 0    x_2 0   2x_1 0   0   0    0   |
     | 0   0   0    0   0    0    0   2x_0 x_1 x_2 0    0   x_1 0    0   |
     | 0   0   0    0   0    0    0   0    0   0   x_0  x_1 0   x_2  0   |
     | 0   0   0    0   0    0    0   0    0   0   0    0   x_0 2x_1 x_2 |

             ZZ             8       ZZ             15
o1 : Matrix (--[x , x , x ])  <--- (--[x , x , x ])
              5  0   1   2           5  0   1   2
i2 : res coker oo -- resolve this map

      ZZ             8      ZZ             15      ZZ             10      ZZ             3
o2 = (--[x , x , x ])  <-- (--[x , x , x ])   <-- (--[x , x , x ])   <-- (--[x , x , x ])  <-- 0
       5  0   1   2          5  0   1   2           5  0   1   2           5  0   1   2         
                                                                                               4
     0                     1                      2                      3

o2 : ChainComplex
i3 : betti oo -- check that the resolution is pure (will not be pure for all characteristics)

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

o3 : BettiTally

See also

Ways to use saturatePieri :