Computer calculations for "Some singular curves in Mukai's model of \(\overline{M}_7\)", Section 6

Code 6.2: Dimension of \(T\) invariants in \( \operatorname{Sym}^{4} \Lambda^7 S^{+} \)

Magma V2.27-8     Fri Apr 14 2023 17:06:10 on MAC-M26AQ05N [Seed = 3432081585]

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Type ? for help.  Type -D to quit.
> R:=RootDatum("D5" : Isogeny := "SC");
> DecomposeExteriorPower(R,7,[0,0,0,1,0]);
[
    (1 0 1 0 1),
    (3 0 0 1 0)
]
[ 1, 1 ]
> D:=LieRepresentationDecomposition(R,[[1,0,1,0,1],[3,0,0,1,0]],[1,1]);
> X:=SymmetricPower(D,4);
> Wts,Mults:=WeightsAndMultiplicities(X);                                       
> ZeroWeightSpaceDimension:=function(R,w)
function>      W,M:=DominantWeights(R,w);
function>      return M[#M];
function> end function;
> Z:=[ZeroWeightSpaceDimension(R,Wts[i]): i in [1..#Wts]];
> Dot := function(M,N)
function>   n:=#M;
function>   ans:=0;  
function>   for i:=1 to n do
function|for>      ans:=ans+M[i]*N[i];
function|for>   end for;
function> return ans;
function> end function;  
> Dot(Z,Mults);
359317176120