# Existence of Kirillov--Reshetikhin crystals for multiplicity free nodes

## TL;DR

This paper proves the existence of Kirillov--Reshetikhin crystals for certain nodes where the associated modules decompose multiplicity-free, advancing understanding in quantum group representations.

## Contribution

It establishes the existence of Kirillov--Reshetikhin crystals for nodes with multiplicity-free classical decompositions, a previously unresolved case.

## Key findings

- Existence of $B^{r,s}$ for multiplicity-free nodes
- Clarification of conditions for crystal existence
- Progress in quantum group representation theory

## Abstract

We show that the Kirillov--Reshetikhin crystal $B^{r,s}$ exists when $r$ is a node such that the Kirillov--Reshetikhin module $W^{r,s}$ has a multiplicity free classical decomposition.