# Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types

## TL;DR

This paper proves the existence of crystal pseudobases for certain Kirillov-Reshetikhin modules in exceptional affine types, using bilinear form evaluations and global bases of extremal weight modules.

## Contribution

It establishes the existence of crystal pseudobases for near adjoint node modules in exceptional types, extending previous results to new cases.

## Key findings

- Existence of crystal pseudobases for specific modules in types E6, E7, E8, F4, and E6^{(2)}.
- Application of Kang et al.'s criterion using bilinear form evaluations.
- Use of global bases of extremal weight modules to facilitate proofs.

## Abstract

We prove that, in types $E_{6,7,8}^{(1)}$, $F_4^{(1)}$ and $E_6^{(2)}$, every Kirillov--Reshetikhin module associated with the node adjacent to the adjoint one (near adjoint node) has a crystal pseudobase, by applying the criterion introduced by Kang et.al. In order to apply the criterion, we need to prove some statements concerning values of a bilinear form. We achieve this by using the global bases of extremal weight modules.