applyDualPieriColumn -- apply dualPieriColumn to a single basis pair (wedge_poly, T_lambda)

• Usage:

  applyDualPieriColumn((mu, cols), poly, T, n)

  applyDualPieriColumn(..., Convention => "Row" | "Filling" | "Weyl")

• Inputs:
  • (mu, cols), a sequence, the data passed to dualPieriColumn
  • poly, a ring element, a homogeneous degree-$d$ wedge polynomial
  • T, a basic list, a tableau of shape $\lambda$. May be a List or a Filling (interpreted in the natural form of the convention; see applyPieri).
  • n, an integer, $\dim V$
• Optional inputs:
  • Convention => a string, default value "Filling"
• Outputs:
  • a list, a list of pairs {coefficient, T_mu} representing the image in $S_\mu V$

i1 : needsPackage "SchurFunctors";

i2 : P = QQ[e_0..e_2, SkewCommutative => true];

i3 : sfStdTab = value (SchurFunctors#"private dictionary"#"standardTableaux");

i4 : T = (sfStdTab(3, {1,1}))#0;

i5 : applyDualPieriColumn(({2,1}, {1}), e_0, T, 3)

o5 = {}

o5 : List