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

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Hage, Nohra

Edité par HAL CCSD

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-rowedarray 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 thenotion of super Littlewood–Richardson skew tableaux and we give another combinatorial interpretation of the super Littlewood–Richardson rule.

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