Article Dans Une Revue Journal of Algebraic Combinatorics Année : 2026

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

Résumé

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 by a matrix-ball construction, showing the symmetry property in complete generality. We deduce a combinatorial version of the super Littlewood–Richardson rule on super Schur functions over a finite signed alphabet. Finally, we introduce the notion of super Littlewood–Richardson skew tableaux and we give another combinatorial interpretation of the super Littlewood–Richardson rule.

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Dates et versions

hal-03710691 , version 1 (30-06-2022)
hal-03710691 , version 2 (29-09-2022)
hal-03710691 , version 3 (17-05-2026)

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Nohra Hage. A super Robinson–Schensted–Knuth correspondence with symmetry and the super Littlewood–Richardson rule. Journal of Algebraic Combinatorics, 2026, pp.55. ⟨10.1007/s10801-026-01524-9⟩. ⟨hal-03710691v3⟩

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