Rigged Configurations for all Symmetrizable Types

2015/09/30 by Ben Salisbury, Travis Scrimshaw · 11 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Affine transformation #Algebraic structures and combinatorial models #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Type (biology) #math.CO #math.RT #msc:05E10 #msc:17B37

paper · pdf · open access · doi:10.37236/6028

published in The Electronic Journal of Combinatorics 24(1) (Electronic Journal of Combinatorics) · 10 pages, 1 figure

arxiv created 2017/02/17 · openalex publication_date 2017/02/17 · arxiv updated 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• On crystal bases of the Q-analogue of universal enveloping algebras
• Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits
• Paths and Root Operators in Representation Theory
• B₂-crystals: axioms, structure, models

Cited by

• Rigged configurations and the ⁎-involution for generalized Kac–Moody algebras
• A new description of the bicrystal B(∞) and the extended crystal