On the span of supersymmetric Young tableaux.

De Concini et al. [De Concini, C., Eisenbud, D. & Procesi, C. (1980) Invent. Math. 56, 129-165] have established for classical Young bitableaux the fact that the span of all bitableaux of shape lambda over the rationals includes all bitableaux of all shapes mu > lambda. We extend their result to the more general setting of supersymmetric Young tableaux. Our proof, even in the classical case, has the advantage of providing an explicit combinatorial algorithm for the computation of the coefficients.

德孔西尼（De Concini）等人在文献[De Concini, C., Eisenbud, D. & Procesi, C. (1980) Invent. Math. 56, 129-165]中，针对经典Young双表格（Young bitableaux）证明了下述事实：有理数域上形状为λ的全体双表格的张成空间，包含所有形状μ>λ的双表格。我们将这一结论推广至更一般的超对称Young表格（supersymmetric Young tableaux）研究框架中。即便在经典情形下，我们的证明方法仍具备独到优势——它可提供一种用于系数计算的显式组合算法。