Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Some bijective correspondences involving domino tableaux. | Some bijective correspondences involving domino tableaux Marc A. A. van Leeuwen Université de Poitiers Departement de Mathématiques UFR Sciences SP2MI Teleport 2 BP 30179 86962 Futuroscope Chasseneuil Cedex France maavl@ URL http maavl Submitted April 13 2000 Accepted July 11 2000. ABSTRACT We define a number of new combinatorial operations on skew semistandard domino tableaux that complement constructions defined by C. Carré and B. Leclerc and clarify the link with ordinary skew semistandard tableaux and the Littlewood-Richardson rule. These operations are 1 a bijection between semistandard domino tableaux and certain pairs of ordinary tableaux of the same weight that together fill the same shape and which determine the plactic class of the domino tableau 2 a weight preserving reversible transformation of domino tableaux into ordinary tableaux of a related shape the correspondence involves 2-quotients mapping the subset of Yamanouchi domino tableaux onto that of the Littlewood-Richardson tableaux 3 a correspondence between Yamanouchi domino tableaux of shape A and weight p and Yamanouchi domino tableaux of shape p and weight A where p is p scaled horizontally and vertically by a factor 2. The essential properties of 1 and 2 are obtained by proving their commutation with the coplactic or crystal operations which for domino tableaux were defned by Carreé and Leclerc . Construction 2 allows algorithmic separation of the Littlewood-Richardson tableaux describing the decomposition of the tensor square of a general linear group representation into contributions to its symmetric and alternating parts. Mathematics Subject Classification 2000 05E10. Keywords and Phrases domino tableau bijective proof. 1. Introduction. The oldest form of the Robinson-Schensted correspondence given in Rob associates to any semistandard skew tableaux T of shape x p and weight a a pair L P consisting for some partition V of a .
