A crystal to rigged configuration bijection and the filling map for type D4(3)

Travis Scrimshaw

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We give a bijection Φ from rigged configurations to a tensor product of Kirillov-Reshetikhin crystals of the form Br,1 and B1,s in type D4(3). We show that the cocharge statistic is sent to the energy statistic for tensor products i=1NBri,1 and i=1NB1,si. We extend this bijection to a single Br,s, show that it preserves statistics, and obtain the so-called Kirillov-Reshetikhin tableaux model for Br,s. Additionally, we show that Φ commutes with the virtualization map and that B1,s is naturally a virtual crystal in type D4(1), thus defining an affine crystal structure on rigged configurations corresponding to B1,s.

Original languageEnglish (US)
Pages (from-to)294-349
Number of pages56
JournalJournal of Algebra
Volume448
DOIs
StatePublished - Feb 15 2016

Keywords

  • Crystal
  • Quantum group
  • Rigged configuration

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