Super jeu de taquin and combinatorics of super tableaux of type A

This paper presents a combinatorial study of the super plactic monoid type A, which is related to representations general linear Lie superalgebra. We introduce analogue Schützenberger’s jeu de taquin on structure tableaux over signed alphabet. show that this procedure transforms skew into Young compatible with congruence and it confluent. deduce properties relating insertion algorithms tableaux. Moreover, we evacuation as an involution its compatibility congruence. Finally, describe in terms Fomin’s growth diagrams order give version Littlewood–Richardson rule.