Geodesic
An analogue of Jeu de taquin for Littelmann's crystal paths
Séminaire lotharingien de combinatoire, Tome 41 (1998)

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Littelmann has given a combinatorial model for the characters of representations of semisimple Lie algebras, in terms of certain paths traced in the space of (rational) weights. From it, a description of the decomposition of tensor products can be derived that generalises the Littlewood-Richardson rule (the latter is valid in type A(n) only). We present a new combinatorial construction that expresses in a bijective manner the symmetry of the tensor product in this path model. In type A(n), where there is a correspondence between paths and skew tableaux, this construction is equivalent to Schützenberger's jeu de taquin; in the general case the construction retains its most crucial properties of symmetry and confluence. 

@article{SLC_1998_41_a1,
     author = {Marc A. A. van Leeuwen},
     title = {An analogue of {Jeu} de taquin for {Littelmann's} crystal paths},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {41},
     year = {1998},
     url = {http://geodesic.mathdoc.fr/item/SLC_1998_41_a1/}
}
TY  - JOUR
AU  - Marc A. A. van Leeuwen
TI  - An analogue of Jeu de taquin for Littelmann's crystal paths
JO  - Séminaire lotharingien de combinatoire
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VL  - 41
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1998_41_a1/
ID  - SLC_1998_41_a1
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%0 Journal Article
%A Marc A. A. van Leeuwen
%T An analogue of Jeu de taquin for Littelmann's crystal paths
%J Séminaire lotharingien de combinatoire
%D 1998
%V 41
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1998_41_a1/
%F SLC_1998_41_a1
Marc A. A. van Leeuwen. An analogue of Jeu de taquin for Littelmann's crystal paths. Séminaire lotharingien de combinatoire, Tome 41 (1998). http://geodesic.mathdoc.fr/item/SLC_1998_41_a1/