Séminaire Lotharingien de Combinatoire, B20b (1988), 11 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 372/S-20, p. 57-78.]

Marie-Pierre Delest, Serge Dulucq and Luc Favreau

An analogue to Robinson-Schensted correspondence for oscillating tableaux

Abstract. We give the hook formula for oscillating tableaux of length n and final shape l, and using a bijective proof we construct an analogue of the Robinson-Schensted correspondence to prove the dimension identity

1.3.5...(2n-1)=\sum_\lambda(fn\lambda)2

related to the irreducible representation of the Brauer algebra of the symplectic group. This correspondence turns out to have most of the ordinary Robinson-Schensted correspondence properties.


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