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<p>The Robinson–Schensted–Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of nonnegative integers and pairs of same-shape semistandard tableaux. This correspondence satisfies the symmetry property, that is, exchanging the rows of a two-rowed array is equivalent to exchanging the positions of the corresponding pair of semistandard tableaux. In this article, we introduce a super analogue of the RSK correspondence for super tableaux over a signed alphabet using a super version of Schensted’s insertion algorithms. We give a geometrical interpretation of the super RSK correspondence via a matrix ball construction, showing the symmetry property in complete generality. Finally, we deduce a combinatorial version of the super Littlewood–Richardson rule for super Schur functions over a finite signed alphabet.</p>

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A super Robinson–Schensted–Knuth correspondence with symmetry and the super Littlewood–Richardson rule

  • 期刊论文

  • 发表日期：

    2026年5月16日

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  • Nohra Hage

摘要

The Robinson–Schensted–Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of nonnegative integers and pairs of same-shape semistandard tableaux. This correspondence satisfies the symmetry property, that is, exchanging the rows of a two-rowed array is equivalent to exchanging the positions of the corresponding pair of semistandard tableaux. In this article, we introduce a super analogue of the RSK correspondence for super tableaux over a signed alphabet using a super version of Schensted’s insertion algorithms. We give a geometrical interpretation of the super RSK correspondence via a matrix ball construction, showing the symmetry property in complete generality. Finally, we deduce a combinatorial version of the super Littlewood–Richardson rule for super Schur functions over a finite signed alphabet.