Rigged configurations for all symmetrizable types

Ben Salisbury, Travis Scrimshaw

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In an earlier work, the authors developed a rigged configuration model for the crystal B(∞) (which also descends to a model for irreducible highest weight crystals via a cutting procedure). However, the result obtained was only valid in finite types, affine types, and simply-laced indefinite types. In this paper, we show that the rigged configuration model proposed does indeed hold for all symmetrizable types. As an application, we give an easy combinatorial condition that gives a Littlewood- Richardson rule using rigged configurations which is valid in all symmetrizable Kac- Moody types.

Original languageEnglish (US)
Article number#P1.30
JournalElectronic Journal of Combinatorics
Volume24
Issue number1
DOIs
StatePublished - Feb 17 2017

Bibliographical note

Funding Information:
Partially supported by CMU Early Career grant #C62847 and by Simons Foundation grant #429950. Partially supported by NSF grant OCI-1147247 and RTG grant NSF/DMS-1148634.

Publisher Copyright:
© 2017, Australian National University. All rights reserved.

Keywords

  • Crystal
  • Littlewood-Richardson rule
  • Rigged configuration

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