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Tableau
A Young-tableau object with unlabelled boxes.
Declares that the object carrying this property is used to label a Young tableau with
unlabelled boxes (Young diagram). The arguments of such objects denote the lenghts of the rows.
The dimension argument of the property sets the dimension.
Can be used in combination with the lr_tensor and tab_dimension algorithms
to compute tensor product representations.\tableau{#}::FilledTableau(dimension=3);
ex:=\tableau{c,c}{c}\tableau{a,a}{b};
lr_tensor(_);
\(\displaystyle{}\text{Attached property FilledTableau to }\ytableaushort{{\#}}.\)
\(\displaystyle{}\ytableaushort{{c}{c},{c}} \otimes \ytableaushort{{a}{a},{b}}\)
\tableau({c, c} , c) \tableau({a, a} , b)
\(\displaystyle{}\ytableaushort{{c}{c}{a}{a},{c}{b}} \oplus \ytableaushort{{c}{c}{a}{a},{c},{b}} \oplus \ytableaushort{{c}{c}{a},{c}{a}{b}} \oplus \ytableaushort{{c}{c}{a},{c}{a},{b}} \oplus \ytableaushort{{c}{c}{a},{c}{b},{a}} \oplus \ytableaushort{{c}{c},{c}{a},{a}{b}}\)
\tableau({c, c, a, a} , {c, b}) + \tableau({c, c, a, a} , c , b) + \tableau({c, c, a} , {c, a, b}) + \tableau({c, c, a} , {c, a} , b) + \tableau({c, c, a} , {c, b} , a) + \tableau({c, c} , {c, a} , {a, b})
q=[int(tab_dimension(t.ex())) for t in ex.top().terms()];
{}$\big[$$
27$, $10$, $10$, $8$, $8$, $1$$\big]$