Perfectness of Kirillov-Reshetikhin Crystals $B^{r,s}$ for types $E_6^{(1)}$ and $E_7^{(1)}$ with a minuscule node $r$

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 $s\ge 1$ using the polytope model of KR crystals introduced by Jang.

17 pages; typo fixed; proofs improved

References in corpus (3)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Demazure structure inside Kirillov-Reshetikhin crystals
• A combinatorial realization of Kirillov-Reshetikhin crystals for type E arising from translations