Domino tableaux, Schutzenberger involution, and the symmetric group action

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.

PlainTeX, 11 pages. Revised version contains minor corrections and additional references