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Brant Jones ; Anne Schilling - Affine structures and a tableau model for E6 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 E6 crystalsConference paper

Authors: Brant Jones 1; Anne Schilling 1

  • 1 Department of Mathematics [Univ California Davis]

We provide the unique affine crystal structure for type E(1)6 Kirillov―Reshetikhin crystals corresponding to the multiples of fundamental weights sΛ1,sΛ2, and sΛ6 for all s1 (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(1)6 Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E(1)7 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,typeE6,[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
  • EMSW21-VIGRE: Focus on Mathematics; Funder: National Science Foundation; Code: 0636297
  • FRG: Collaborative Research: Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects; Funder: National Science Foundation; Code: 0652641

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