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  1. Home > Articles & Issues >
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  3. Rigged configuration ...
Conference paper

Rigged configurations of type $D_4^{(3)}$ and the filling map

Travis Scrimshaw ORCID (1)
(1) University of California [Davis]
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Imported on
November 21, 2016
Published on
December 31, 2014
Last modified on
March 31, 2025
Volume
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Proceedings
DOI
10.46298/dmtcs.2494
License
Attribution 4.0 International (CC BY 4.0)
National Science Foundation
1147247
Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics
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Rigged configurations of type $D_4^{(3)}$ and the filling map

Travis Scrimshaw ORCID (1)
(1) University of California [Davis]
Abstract
English
We give a statistic preserving bijection from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals $\otimes_{i=1}^{N}B^{1,s_i}$ in type $D_4^{(3)}$ by using virtualization into type $D_4^{(1)}$. We consider a special case of this bijection with $B=B^{1,s}$, and we obtain the so-called Kirillov–Reshetikhin tableaux model for the Kirillov–Reshetikhin crystal.
French
Nous donnons une bijection prservant les statistiques entre les configurations gréées et les produits tensoriels de cristaux de Kirillov–Reshetikhin $\otimes_{i=1}^{N}B^{1,s_i}$ de type $D_4^{(3)}$, via une virtualisation en type $D_4^{(1)}$. Nous considérons un cas particulier de cette bijection pour $B=B^{1,s}$ et obtenons ainsi les modèles de tableaux appelés Kirillov–Reshetikhin pour le cristal Kirillov–Reshetikhin.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • rigged configuration
  • Kirillov–Reshetikhin crystal
  • bijection
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