A super Robinson–Schensted–Knuth correspondence with symmetry and the super Littlewood–Richardson rule - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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)

Identifiants

  • HAL Id : hal-03710691 , version 1

Citer

Nohra Hage. A super Robinson–Schensted–Knuth correspondence with symmetry and the super Littlewood–Richardson rule. 2022. ⟨hal-03710691v1⟩
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