Type Dn(1) rigged configuration bijection

Masato Okado, Reiho Sakamoto, Anne Schilling, Travis Scrimshaw

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov–Reshetikhin crystals of type Dn(1) in full generality. We prove the invariance of rigged configurations under the action of the combinatorial R-matrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type Dn(1). In addition, we establish that the bijection is a classical crystal isomorphism.

Original languageEnglish (US)
Pages (from-to)341-401
Number of pages61
JournalJournal of Algebraic Combinatorics
Volume46
Issue number2
DOIs
StatePublished - Sep 1 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Keywords

  • Crystal bases
  • Fermionic formula
  • Kyoto path model
  • Rigged configurations

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