pureFree -- computes an GL(V)-equivariant map whose resolution is pure, or the reduction mod p of such a map

Synopsis

• Usage:

  pieri(List, Module)
  pieri(List, Module, ZZ)

• Inputs:

  • d, a list, a list of degrees (increasing numbers)
  • V, a module, an n-dimensional vector space over a field of char 0
  • p, an integer, a characteristic, the output is over the field ZZ/p
• Outputs:

  • a matrix, Either calls pieri or saturatePieri depending on if the argument p is given. The result is a map whose cokernel has Betti diagram with degree sequence d if p is not given, and is the same map reduced mod p if it is given.

Description

i1 : betti res coker pureFree({0,1,2,4},QQ^3) -- degree sequence {0,1,2,4}

            0 1 2 3
o1 = total: 3 8 6 1
         0: 3 8 6 .
         1: . . . 1

o1 : BettiTally

i2 : betti res coker pureFree({0,1,2,4},QQ^3,2) -- same map, but reduced mod 2

            0 1 2 3
o2 = total: 3 8 6 1
         0: 3 8 6 .
         1: . . . 1

o2 : BettiTally

See also

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