Perfectness of Kirillov-Reshetikhin Crystals $B^{r,s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with a minuscule node $r$

TL;DR

This paper proves the perfectness of Kirillov-Reshetikhin crystals for specific affine types with minuscule nodes, using a polytope model, advancing understanding in crystal base theory.

Contribution

It establishes the perfectness of KR crystals for types E6^(1) and E7^(1) with minuscule nodes, employing a novel polytope model approach.

Findings

Confirmed perfectness of B^{r,s} for E6^(1) and E7^(1)

Applied polytope model to analyze crystal structures

Extended the theory of KR crystals in affine types

Abstract

We prove the perfectness of Kirillov-Reshetikhin crystals $B^{r,s}$ for types $E_{6}^{(1)}$ and $E_{7}^{(1)}$ with $r$ being the minuscule node and $s\geq 1$ using the polytope model of KR crystals introduced by Jang.