TY - JOUR
T1 - Rigged configurations for all symmetrizable types
AU - Salisbury, Ben
AU - Scrimshaw, Travis
N1 - 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.
PY - 2017/2/17
Y1 - 2017/2/17
N2 - 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.
AB - 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.
KW - Crystal
KW - Littlewood-Richardson rule
KW - Rigged configuration
UR - http://www.scopus.com/inward/record.url?scp=85013408590&partnerID=8YFLogxK
U2 - 10.37236/6028
DO - 10.37236/6028
M3 - Article
AN - SCOPUS:85013408590
SN - 1077-8926
VL - 24
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 1
M1 - #P1.30
ER -