Geodesic
Stable rigged configurations and Littlewood―Richardson tableaux
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011).

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For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type $A$ can be expressed as a sum of that of type $A$ with Littlewood–Richardson coefficients. Combining this result with theorems of Kirillov–Schilling–Shimozono and Lecouvey–Okado–Shimozono, we settle the $X=M$ conjecture under the large rank hypothesis. 
@article{DMTCS_2011_special_260_a61,
     author = {Okado, Masato and Sakamoto, Reiho},
     title = {Stable rigged configurations and {Littlewood{\textemdash}Richardson} tableaux},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)},
     year = {2011},
     doi = {10.46298/dmtcs.2948},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2948/}
}
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%J Discrete mathematics & theoretical computer science
%D 2011
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Okado, Masato; Sakamoto, Reiho. Stable rigged configurations and Littlewood―Richardson tableaux. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) (2011). doi : 10.46298/dmtcs.2948. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2948/

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