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Domino tableaux, Schutzenberger involution, and the symmetric group action

Arkady Berenstein·Anatol N. Kirillov
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Abstract

We define an action of the symmetric group on the set of domino tableaux, and prove that the number of domino tableaux of a given weight does not depend on the permutation of components of the last. A bijective proof of the well-known result due to J. Stembridge that the number of self-evacuating tableaux of a given shape is equal to that of domino tableaux of the same shape is given.

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Arkady Berenstein, Anatol N. Kirillov. 1997-09-15. Domino tableaux, Schutzenberger involution, and the symmetric group action. https://arxiv.org/abs/q-alg/9709010

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