Rigged configurations for all symmetrizable types

Ben Salisbury; Travis Scrimshaw

doi:10.37236/6028

Rigged configurations for all symmetrizable types

Ben Salisbury, Travis Scrimshaw

School of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English (US)
Article number	#P1.30
Journal	Electronic Journal of Combinatorics
Volume	24
Issue number	1
DOIs	https://doi.org/10.37236/6028
State	Published - Feb 17 2017

Bibliographical note

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.

Keywords

Crystal
Littlewood-Richardson rule
Rigged configuration

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10.37236/6028

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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.",

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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.

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Rigged configurations for all symmetrizable types

Abstract

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