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indexMonomial(YoungTableau,YoungTableau,PolynomialRing) -- a monomial that represents an index tableau

Description

The index monomial is used in the construction of higher Specht polynomials. To calculate the index monomial first the index tableau of $S$, $i(S)$ is calculated. Then the monomial is calculated as $x_T^{i(S)}$. This is a monomial with the variables as they appear in T with the exponents that appear in $i(S)$.

i1 : R = QQ[x_0..x_4]

o1 = R

o1 : PolynomialRing
 
i2 : p = new Partition from {2,2,1}

o2 = Partition{2, 2, 1}

o2 : Partition
 
i3 : S  = youngTableau(p,{0,2,1,3,4})

o3 = | 0 2 |
     | 1 3 |
     | 4 |

o3 : YoungTableau
 
i4 : T  = youngTableau(p,{0,1,2,3,4})

o4 = | 0 1 |
     | 2 3 |
     | 4 |

o4 : YoungTableau
 
i5 : ind = indexTableau(S)

o5 = | 0 1 |
     | 1 2 |
     | 3 |

o5 : YoungTableau
 
i6 : indexMonomial(S,T,R)

          2 3
o6 = x x x x
      1 2 3 4

o6 : R

See also

Ways to use this method:

The source of this document is in SpechtModule.m2:3305:0.