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arXiv · 2206.15451

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

Nohra Hage
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Abstract

The Robinson-Schensted-Knuth (RSK) correspondence is a bijective correspondence between two-rowed arrays of non-negative 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.

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Nohra Hage. 2022-06-30. A super Robinson-Schensted-Knuth correspondence with symmetry and the super Littlewood-Richardson rule. https://doi.org/10.1007/s10801-026-01524-9

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