Abstract
In this paper, we study the shape and the reduced shape algebra for the Lie superalgebra \({\mathfrak {sl}}(m,n)\). We define quasistandard Young tableaux, and they give a combinatorial basis for the reduced shape algebra, called the diamond cone. There is a natural bijective map from the set of semistandard tableaux with shape \(\lambda \) to the set of quasistandard tableaux with smaller shape: the diamond cone is compatible with the stratification of the reduced shape algebra.
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