applyDualLR -- apply dualLR to a single basis pair (T_nu, T_mu)

• Usage:

  applyDualLR((lambda, mu, nu), Q, {T_nu, T_mu}, n)

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

• Inputs:
  • (lambda, mu, nu), a sequence
  • Q, a list, an LR tableau
  • {T_nu, T_mu}, a list, a 2-element list containing the source basis pair (a tableau of shape $\nu$ and a tableau of shape $\mu$). Each may be a List or a Filling, interpreted in the natural form of the convention (see applyPieri), independently.
  • n, an integer
• Optional inputs:
  • Convention => a string, default value "Row"
• Outputs:
  • a list, list of pairs {coefficient, T_lambda} representing the image in $S_\lambda V$

i1 : shapes = ({2,1}, {1}, {1,1});

i2 : Q = (lrTableaux shapes)#0;

i3 : applyDualLR(shapes, Q, {{{0},{1}}, {{0},{}}}, 3)

       1
o3 = {{-, {{0, 0}, {1}}}}
       3

o3 : List