Super jeu de taquin and the super Littlewood—Richardson rule

par Nohra Hage (Lille)

jeudi 2 juin 2022, 14:00 → 15:00 Europe/Paris

C 112 (St-Etienne Métare )

We introduce a super version of the Schützenberger's jeu de taquin on super Young tableaux over a signed alphabet. We show that this procedure which transforms super skew tableaux into super Young tableaux is confluent and it is compatible with the super plactic monoid of type A, which is related to the representations of the general linear Lie superalgebra. We deduce properties relating the super jeu de taquin to insertion algorithms on super tableaux. Moreover, we introduce a super version of the Robinson—Schensted—Knuth correspondence for super tableaux and we give a combinatorial version of the super Littlewood--Richardson rule. Finally, we show how the super plactic monoid of type A can be studied by a rewriting approach.