Masato Okado ; Reiho Sakamoto - Stable rigged configurations and Littlewood―Richardson tableaux

dmtcs:2948 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2948
Stable rigged configurations and Littlewood―Richardson tableauxArticle

Authors: Masato Okado 1; Reiho Sakamoto 2

  • 1 Department of Mathematical Science
  • 2 Department of Physics [Tokyo]

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.

https://doi.org/10.46298/dmtcs.2948
Source: HAL:hal-01215070v1
Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: affine crystals,rigged configurations,Littlewood―Richardson tableaux,fermionic formula,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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