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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A symplectic jeu de taquin bijection between
the tableaux of King and of De Concini


Author: Jeffrey T. Sheats
Journal: Trans. Amer. Math. Soc. 351 (1999), 3569-3607
MSC (1991): Primary 05E15, 22E46
Published electronically: April 26, 1999
MathSciNet review: 1466956
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Abstract: The definitions, methods, and results are entirely combinatorial. The symplectic jeu de taquin algorithm developed here is an extension of Schützenberger's original jeu de taquin and acts on a skew form of De Concini's symplectic standard tableaux. This algorithm is used to construct a weight preserving bijection between the two most widely known sets of symplectic tableaux. Anticipated applications to Knuth relations and to decomposing symplectic tensor products are indicated.


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Additional Information

Jeffrey T. Sheats
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Address at time of publication: 7364 E10th Avenue, Denver, Colorado 80220

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02166-2
PII: S 0002-9947(99)02166-2
Received by editor(s): July 1, 1997
Published electronically: April 26, 1999
Additional Notes: This research was supported in part by NSA Grants MDA 904-92-H-3061 and MDA 904-95-H-1018
Article copyright: © Copyright 1999 American Mathematical Society