standardWeylTableaux -- all Weyl-semistandard tableaux of a given shape

• Usage:

  standardWeylTableaux(d, lambda)

• Inputs:
  • d, an integer, the size of the alphabet $\{0,\ldots,d-1\}$
  • lambda, a list, a partition (the shape of the tableau)
• Outputs:
  • a list, all Weyl-semistandard WeylFillings of shape $\lambda$ with entries in $\{0,\ldots,d-1\}$

i1 : SW = standardWeylTableaux(3, {2,1});

i2 : #SW

o2 = 8

i3 : rank weylModule({2,1}, QQ^3)

o3 = 8

i4 : standardWeylTableaux(2, {2})

      +-+-+  +-+-+  +-+-+
o4 = {|0|0|, |0|1|, |1|1|}
      +-+-+  +-+-+  +-+-+

o4 : List

i5 : standardWeylTableaux(3, {1,1,1})

      +-+
o5 = {|0|}
      |1|
      |2|
      +-+

o5 : List