Virtualization map for the Littelmann path model

TL;DR

This paper demonstrates that the virtualization map for the Littelmann path model, derived from diagram folding, provides a unified proof that certain Kirillov--Reshetikhin crystals are compatible with diagram foldings, confirming a conjecture.

Contribution

It introduces a natural embedding of weight lattices as a virtualization map for the Littelmann path model, offering a type-independent proof of crystal folding compatibility.

Findings

Virtualization map recovers Kashiwara's result.

Type-independent proof for Kirillov--Reshetikhin crystals.

Confirms a conjecture by Okado, Schilling, and Shimozono.

Abstract

We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.