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.
Bibliographical noteFunding 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.
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- Littlewood-Richardson rule
- Rigged configuration