Geodesic
An analogue to Robinson-Schensted correspondence for oscillating tableaux
Séminaire lotharingien de combinatoire, Tome 20 (1988) 
Marie-Pierre Delest; Serge Dulucq; Luc Favreau. An analogue to Robinson-Schensted correspondence for oscillating tableaux. Séminaire lotharingien de combinatoire, Tome 20 (1988). http://geodesic.mathdoc.fr/item/SLC_1988_20_a1/
@article{SLC_1988_20_a1,
     author = {Marie-Pierre Delest and Serge Dulucq and Luc Favreau},
     title = {An analogue to {Robinson-Schensted} correspondence for oscillating tableaux},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1988},
     volume = {20},
     url = {http://geodesic.mathdoc.fr/item/SLC_1988_20_a1/}
}
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AU  - Luc Favreau
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JO  - Séminaire lotharingien de combinatoire
PY  - 1988
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ID  - SLC_1988_20_a1
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%A Serge Dulucq
%A Luc Favreau
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Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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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