Character Array -- homological shift

Synopsis

Shift the homological degrees of a character.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x*y,x*z,y*z)

o2 = ideal (x*y, x*z, y*z)

o2 : Ideal of R

i3 : RI = res I

      1      3      2
o3 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o3 : ChainComplex

i4 : S3 = symmetricGroupActors R

o4 = {| y z x |, | y x z |, | x y z |}

o4 : List

i5 : A = action(RI,S3)

o5 = ChainComplex with 3 actors

o5 : ActionOnComplex

i6 : a = character A

o6 = Character over R
      
     (0, {0}) => | 1 1 1 |
     (1, {2}) => | 0 1 3 |
     (2, {3}) => | -1 0 2 |

o6 : Character

i7 : a[-10]

o7 = Character over R
      
     (10, {0}) => | 1 1 1 |
     (11, {2}) => | 0 1 3 |
     (12, {3}) => | -1 0 2 |

o7 : Character