applyPieri -- apply pieri to a single source tableau T_mu

• Usage:

  applyPieri((mu, boxes), T, P)

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

• Inputs:
  • (mu, boxes), a sequence, the same data passed to pieri
  • T, a basic list, a tableau of shape $\mu$. May be a List or a Filling. In "Row"/"Weyl" convention a List is the PM row form; in "Filling" convention a List is column form (auto-wrapped). A Filling is always treated as column form.
  • P, a polynomial ring, whose generators carry $\mathrm{Sym}^d V$
• Optional inputs:
  • Convention => a string, default value "Row"
• Outputs:
  • a list, a list of pairs {poly, T_lambda} where each poly is a homogeneous degree-$d$ form and $T_\lambda$ is a standard tableau of $\lambda$; the image is $\sum \mathrm{poly}_i \otimes T_{\lambda,i}$ in $\mathrm{Sym}^d V \otimes S_\lambda V$

i1 : P = QQ[a,b,c];

i2 : T = (standardTableaux(3, {3,2,1}))#0;

i3 : applyPieri(({3,2,1}, {1}), T, P)

o3 = {{3a, {{0, 0}, {1, 1}, {2}}}}

o3 : List