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{\bf Marc A. A. van Leeuwen}
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{\bf Some Bijective Correspondences Involving Domino \hfil\break
Tableaux}
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We define a number of new combinatorial operations on skew semistandard domino
tableaux that complement constructions defined by C.~Carr\'e 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 $\lambda$ and
weight $\mu$ and Yamanouchi domino tableaux of shape $\mu'$ and weight
$\lambda$, where $\mu'$ is $\mu$ 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 defined by Carr\'e 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.

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