Brant Jones ; Anne Schilling - Affine structures and a tableau model for $E_6$ crystals

dmtcs:2809 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2809
Affine structures and a tableau model for $E_6$ crystalsArticle

Authors: Brant Jones 1; Anne Schilling 1

  • 1 Department of Mathematics [Univ California Davis]

We provide the unique affine crystal structure for type $E_6^{(1)}$ Kirillov―Reshetikhin crystals corresponding to the multiples of fundamental weights $s\Lambda _1, s\Lambda _2$, and $s\Lambda _6$ for all $s≥ 1$ (in Bourbaki's labeling of the Dynkin nodes, where 2 is the adjoint node). Our methods introduce a generalized tableaux model for classical highest weight crystals of type $E$ and use the order three automorphism of the affine $E_6^{(1)}$ Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type $E_7^{(1)}$ Kirillov―Reshetikhin crystals corresponding to the adjoint node.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Affine crystals,Kirillov―Reshetikhin crystals,$type E_6$,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]
Funding:
    Source : OpenAIRE Graph
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652652
  • Combinatorial Aspects of Representation Theory, Mathematical Physics and q-Series; Funder: National Science Foundation; Code: 0501101
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641
  • EMSW21-VIGRE: Focus on Mathematics; Funder: National Science Foundation; Code: 0636297

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