applyPieriColumn -- apply pieriColumn to a single source tableau T_mu

• Usage:

  applyPieriColumn((mu, cols), T, P)

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

• Inputs:
  • (mu, cols), a sequence, the same data passed to pieriColumn
  • T, a basic list, a tableau of shape $\mu$. May be a List or a Filling (interpreted in the natural form of the convention; see applyPieri).
  • P, a polynomial ring, a SkewCommutative ring whose generators carry $\wedge^d V$
• Optional inputs:
  • Convention => a string, default value "Filling"
• Outputs:
  • a list, a list of pairs {wedge_poly, T_lambda} representing the image in $\wedge^d V \otimes S_\lambda V$

i1 : needsPackage "SchurFunctors";

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

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

i4 : F = (sfStdTab(3, {2,1}))#0;

i5 : applyPieriColumn(({2,1}, {1}), F, P)

           +-+-+         +-+-+
o5 = {{e , |0|0|}, {-e , |0|1|}}
        1  +-+-+      0  +-+-+

o5 : List