English

Rigged configurations for all symmetrizable types

Combinatorics 2021-01-25 v2 Representation Theory

Abstract

In an earlier work, the authors developed a rigged configuration model for the crystal B()B(\infty) (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.

Keywords

Cite

@article{arxiv.1509.07833,
  title  = {Rigged configurations for all symmetrizable types},
  author = {Ben Salisbury and Travis Scrimshaw},
  journal= {arXiv preprint arXiv:1509.07833},
  year   = {2021}
}

Comments

10 pages, 1 figure

R2 v1 2026-06-22T11:05:45.526Z