In an earlier work, the authors developed a rigged configuration model for the crystal $B(\infty)$ (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.
@article{10_37236_6028,
author = {Ben Salisbury and Travis Scrimshaw},
title = {Rigged configurations for all symmetrizable types},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6028},
zbl = {1355.05279},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6028/}
}
TY - JOUR
AU - Ben Salisbury
AU - Travis Scrimshaw
TI - Rigged configurations for all symmetrizable types
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6028/
DO - 10.37236/6028
ID - 10_37236_6028
ER -
%0 Journal Article
%A Ben Salisbury
%A Travis Scrimshaw
%T Rigged configurations for all symmetrizable types
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6028/
%R 10.37236/6028
%F 10_37236_6028
Ben Salisbury; Travis Scrimshaw. Rigged configurations for all symmetrizable types. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6028
